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)?

Hint: Think of the smallest non-abelian group you can. Can you find a normal subgroup of this?
