I’m still unclear on what Sumner wanted French to do. Was French’s division supposed to stay behind Sedgwick’s division and follow it into the West Woods, or was it supposed to move to the left and extend the Union line? French clearly thinks that he’s supposed to extend the line left. He doesn’t just wander off.
Things were constantly changing, sometimes minute by minute.
Sumner arrives at the front and discovers that things aren't as he expected when he left for the front. He runs into Hooker (wounded and in great pain) being carried from the field. Sumner asks Hooker what the situation is and Hooker tells him he thinks he has just won a great battle (Hooker would later testify he was in-and-out with the pain and really could not recall much of this.)
At this point, an aide arrives carrying orders from McClellan for Sumner and Hooker. Sumner reads both and it is clear that McClellan's view of the battle does not equate with the situation Sumner sees before him. He hasn't really been able to see the West Woods up until he passes through the East Woods. He does a quick personal recon, sees some Yankee troops near the northern end of the West Woods. At some point he does find out there are troops where Greene is, but I don't recall if he was ever in communication with Greene. Hooker has put Meade, his junior division commander, in charge before leaving. I think Sumner does get in communication with Meade briefly here as he tries to find out what the situation is, but I don't know what Meade would have known in detail about the mess going on where Sumner was.
Sumner's report has little detail:
SIR: I have the honor to report that, on the evening of the 16th ultimo, I received an order at Keedysville to send the Twelfth Corps (Banks') to support General Hooker, and to hold my own, the Second Corps, in readiness to march for the same purpose an hour before daylight. Banks' corps, under General Mansfield, marched at 11.30 p.m., and my own corps was ready to move at the time ordered, but did not receive from headquarters the order to march till 7.20 a.m. on the 17th. I moved Sedgwick's division immediately in three columns on the receipt of the order, followed by French's division in the same order. Richardson was ordered to move in the same direction by the commanding general about an hour later. On arriving at the place where Hooker had been engaged, I found him wounded, and his corps, after a severe contest, had been repulsed. Banks' corps, under the immediate command of General Mansfield, had gone into battle on Hooker's left, and was engaged when I came upon the field. General Mansfield, a worthy and gallant veteran, was unfortunately mortally wounded while leading his corps into action. My First Division (Sedgwick's) went into battle in three lines. After his first line had opened fire for some time, the enemy made a most determined rush to turn our left, and so far succeeded as to break through the line between Banks' corps and my own until they began to appear in our rear. In order to repel this attack from the rear, I immediately faced Sedgwick's third line about, but the fire at that moment became so severe from the left flank that this line moved off in a body to the right, in spite of all the efforts that could be made to stop it. The first and second lines after some time followed this movement, but the whole division was promptly rallied, took a strong position, and maintained it to the close of the battle. Richardson's and French's divisions maintained a furious and successful fight from the time they entered the battle till the end of it, highly to the honor of the officers and soldiers.
Somewhere in the battle (no timestamp) McClellan received this:
To General MCCLELLAN:
Re-enforcements are badly wanted. Our troops are giving way. I am hunting for French's and Slocum's divisions. If you know where they are, send them immediately.
General SUMNER.
French's report doesn't mention Greene at all:
COLONEL: My division, composed of Brig. Gen. Max Weber's and Kimball's brigades, and three regiments of new levies under the command of Col. Dwight Morris (Fourteenth Connecticut), having been in readiness since daybreak on the 17th instant, was put in motion by orders of the general commanding the corps at about 7.30 o'clock a.m. The Antietam Creek was forded by the division, marching in three columns of brigades, Max Weber on the left, the new regiments in the center, and Kimball's brigade on the right. When my left flank had cleared the ford a mile, the division faced to the left, forming three lines of battle adjacent to and contiguous with Sedgwick's, and immediately moved to the front.
The enemy, who was in position in advance, opened his batteries, under which fire my lines steadily moved until the first line, encountering the enemy's skirmishers, charged them briskly, and, entering a group of houses on Roulette's farm, drove back the force, which had taken a strong position for defense. Whilst Max Weber was clearing his front and driving before him the enemy's first line, a sudden and terrible fire was opened upon his right by the troops, which had succeeded in breaking the center division of the line of battle. At the same time a heavy column endeavored to turn my left and rear.
At this moment Captain Sumner communicated to me, from the general commanding the corps, that his right divisions were being severely handled, and directed me to press the enemy with all my force. Appreciating the necessity of the order, without waiting for the new regiments to recover from the disorder incident to their long march in line through woods, corn-fields, and over fences, I left them in reserve, and ordered Kimball to charge to the front. With an unsurpassed ardor this gallant brigade, sweeping over all obstacles, soon crowned the crests of the hills on our left and right, flaunting the regimental banners in defiance to those of the rebels who, flushed with a supposed victory, dared to face us.
If Greene is in between them, you can't see it in those reports. French says his line was contiguous with Sedgwick, but that is pretty hard to picture unless it is before Sedgwick advanced on the West Woods.
Greene's report doesn't mention Sumner, Sedgwick or French at all:
The division was carried into action about 6.30 a.m., under the orders of Brigadier-General Mansfield. As we were going into action the Third Brigade was detached to the right, leaving under my command the First and Second Brigades, with an aggregate of 1,727. The division encountering the enemy in the first woods in our front drove them before it, and, entering the open ground partly covered with corn, moved to the left and took position on the right of the post and rail fence inclosing the field on the right of the burned house (Poffenberger's). There was a battery of brass guns at our left, which we protected. This battery getting out of ammunition for long range was replaced by another.
While in this position the enemy formed in strong force in the woods to the right of the white brick church and advanced on our line. The line was advanced to the axle-trees of the guns, and delivered their fire when the enemy were within 70 yards. They immediately fell back, having suffered immense loss. The division advanced, driving the enemy from the woods near the church and occupying the woods. The Purnell Legion joined us during the action. The Twenty-seventh Indiana was sent to our support, and, after doing good service, retired in consequence of their ammunition being exhausted. The Thirteenth New Jersey then joined the division, and assisted in holding the woods. The position of the division in the advanced woods was very critical. We were in advance of our line on the right and left of us. Sumner's corps, which had advanced on our left, had retired, as had also the troops on our right. Guns were sent for, and a section of Knap's battery arrived, and were ordered to take position on our left. The ground on our left and front was broken and wooded, and concealed the movements of the enemy. I placed the division in line, with the right thrown back, and sent forward skirmishers and sought re-enforcements from General Williams. None were at the time available, and the enemy advancing in large force, threatening to envelop the small command, they were forced to retire. They rallied in the second line of woods. They held the woods by the church nearly two hours, in advance of any other troops in their vicinity. They were in action from 6.30 a.m. to 1.30 p.m.
So if you just go by the official reports, these generals didn't know much at all about what was going on with each other.
LATER: On re-reading, I see that Greene thought Sumner had advanced and then retreated on his left. He apparently doesn't know that the troops that advanced and then retreated on his right were also Sumner's Corps.