Proof that there exists $K \trianglelefteq H $ such that $K$ and $H/K$ are abelian (under certain conditions)

Question

I need some hints to solve the following problem in the context of quotient groups and isomorphism theorems:

Let $N \trianglelefteq G$ with $N$ and $G/N$ abelian groups. Let $H \le G$ be any subgroup of $G$. Proof that there exists $K \trianglelefteq H $ such that $K$ and $H/K$ are abelian groups.

Answer 1

Hint: consider $K=H \cap N$ and apply the second isomorphism theorem.