Hi:

I'll make a straightforward question: Let $\displaystyle G$ be group and $\displaystyle S \leq T \leq G$, these groups satisfying the following conditions:

(a) $\displaystyle T \unlhd G$.

(b) $\displaystyle T$ is simple.

(c) $\displaystyle T$ is a maximal subgroup of$\displaystyle G$.

Is there any other piece of information that can be deduced from these three facts? In particular, can I infer $\displaystyle S \unlhd G$?