If N and every subgroup of N is normal in G then G/N is abelian .

Let $N$ be a normal subgroup of $G$ such that every subgroup of $N$ is normal in $G$ and $C_G(N)\subseteq N $ .Prove that $G/N$ is abelian.

I think we need to use that every subgroup of $N$ is normal in $G$ but i can’t use .Please help me with Hints.

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