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.