Looks like it falls into (and only 3 guns away from one gun in) the range of carbines issued to Company B 10th Illinois Volunteer Cavalry. However, that does not really mean anything, because as seen below, that range covers about 5000 guns. This means the guns were not issued to regiments/units sequentially, as a company of men numbered about 100. So most of the guns in the range went somewhere else, we just don't know where, just like we don't know where your gun went.
C 9471 C 010165CO B 10TH ILL VOL CAV
C 9493 C 010165CO B 10TH ILL VOL CAV
C 9524 C 010165CO B 10TH ILL VOL CAV
C 9556 C 010165CO B 10TH ILL VOL CAV
C 9743 C 010165CO B 10TH ILL VOL CAV
C 9821 C 010165CO B 10TH ILL VOL CAV
C 9845 C 040164CO B 10TH ILL VOL CAV
C 9845 C 010165CO B 10TH ILL VOL CAV
C 9913 C 010165CO B 10TH ILL VOL CAV
C 9947 C 010165CO B 10TH ILL VOL CAV
C10037 C 010165CO B 10TH ILL VOL CAV
C10090 C 010165CO B 10TH ILL VOL CAV
C10090 C 101465CO B 10TH ILL VOL CAV
C10157 C 010165CO B 10TH ILL VOL CAV
C10357 C 010165CO B 10TH ILL VOL CAV
C10387 C 010165CO B 10TH ILL VOL CAV
C10392 C 010165CO B 10TH ILL VOL CAV
C10433 C 010165CO B 10TH ILL VOL CAV
C14781 C 010165CO B 10TH ILL VOL CAV
Would still like to see pictures though.