## Triply Transitive Group Action

Here's a question I'm working on for my Group Theory class:

Suppose $G|X$ is a 3-transitive permutation group. Suppose further that $|X|=n$ is NOT a power of 2, and that $G\ncong S_n$.

Prove or disprove: if $N$ is a proper normal subgroup of $G$, then the action $N|X$ is 2-transitive.

I'm pretty sure the statement is true (taking "proper" to mean $N\neq {e},G$). I'm not really sure where to start though.