Hi all,
A student I'm helping gave me a question.

Q: Give an example of a group G with a normal subgroup N such that N and G/N are abelian, but G is not abelian.

I'm fairly sure there is a dihedral group with this property but i don't have time to find an explicit example.

Can someone help please?

Side note: If we weaken the conditions slightly and replace abelian by solvable no example exists.