Here is what the regulation says:
1516. For Enlisted Men, except companies of Light Artillery-the same as for officers of the respective corps, except that there will be but one feather, the cord will be of worsted, of the same color as that of the facing of the corps, three-sixteenths of an inch in diameter, running three times through a slide of the same material, and terminating with two tassels, not less than two inches long, on the side of the hat opposite the feather. The insignia of corps, in brass, in front of the hat, correspond. ing with those prescribed for officers, with the number of regiment, five. eighths of an inch long, in brass, and letter of company, one inch, in brass,
arranged over insignia.
Brim to be looped up to side of hat with a brass eagle, having a hook attached to the bottom to secure the brim-on the right side for mounted men and left side for foot men. The feather to be worn on the side opposite the loop.