A "different" third isomorphism theorem

Question

I know that, given $H, K \unlhd G$ and $K \leq H$, one has $$\frac{G/K}{H/K} \simeq \frac{G}{H} \, .$$ Under the same hypotheses, is it true that $$\frac{G/K}{G/H} \simeq \frac{H}{K} \quad \huge{?}$$

I think it's wrong, but I can't find a counterexample. If it's true can you deduce it from the previous statement or vice versa?

Answer 1

The best thing you can say is that there is a surjective map $G/K\to G/H$ whose kernel is $H/K$. So instead of cokernels you take kernels.