Is there any characterization of a group $G$ with subgroup $N \lhd G$ such that $G/N \cong N$?

Question

Let $G$ be a finite group and $N$ a normal subgroup of $G$. What do we know about the structure of $G$ if $G/N \cong N$?

I know that some possibilities are that $G \cong N \times N$ or that $G \cong C_{|N|^2}$, but I don't know if that is an exhaustive list.