On composition factors of finite groups having the same set of element orders as the group $U_3(q)$

We study the composition factors of a finite nonsolvable group having the same set of order elements as the simple unitary group $U_3(q)$ for an odd $q$. We prove in particular that for $q>5$ the (only) nonabelian composition factor of such a group is isomorphic to $U_3(q)$.