I want to find groups whose composition factor is isomorphic to the alternating group of order 7, which groups have this condiction? best regards
If you just want some examples, one of the examples is the symmetric group $S_7$ of degree 7. Clearly, you can costruct infinite groups that one of the its composition factors is $A_7$. For example $S_7\times\Bbb Z_p^r$ where $p$ is a prime and $r\geq 0$.