Defining a normal subgroup to be maximal.

Question

I just want to clear up something from Question 2. from the following my professor made:

For Question 2., if $|G|=p$ and $N$ is maximal, does that mean $|N|\neq p$ since there is no subgroup $H$ of $G$ (including $G$ itself) such that $N\leq H\leq G$?