Suppose $G$ is a group and $H_1$, $H_2$, $N$ are subgroups of $G$. $N$ is a normal subgroup of $G$ and $H_2$ is a normal subgroup of $H_1$. Suppose that $H_1/H_2$ is Abelian. Show that $H_1N/H_2N$ is Abelian.
My current thought is using third isomorphism theorem and deduct $H_1N/H_2N$ is a quotient of $H_1/H_2$. However, I just cannot prove $H_1N/H_2N$ is a quotient of $H_1/H_2$. Does my thought wrong?