Is the group $G$ always isomorphic to the group $G/N \times N$? 
Let $N$ be a normal subgroup of $G$. Is the group $G$ always
  isomorphic to the group $G/N \times N$?

I don't think this is true but I can't think of a counter-example. What's an easy counter-example (or way to prove the contrary)?

Consider the cyclic group of order $4$, say $C_{4}$. It has a nornal subgroup $H$ of index 2. $C_{4}/H$ is is a cyclic group of order $2$, isomorphic to $H$! But $H \times H$ is not cyclic!
