Isomorphic Factor Groups

Question

For $H$ and $K$ isomorphic normal subgroups of $G$, factor groups $G/H$ and $G/K$ need not be isomorphic.

But if G is free abelian then does the above still hold?

Answer 1

Consider the case of $G=H=\mathbb{Z}$, and $K=2\mathbb{Z}\subset \mathbb{Z}$. Then $G\cong H\cong K$ but $G/H$ is the trivial group while $G/K=\mathbb{Z}/2\mathbb{Z}$.