If $H$ is a normal subgroup and $N\lt H$, does $NhN=h$ or rather some $h'\in H$

Question

If $H$ is a normal subgroup and $N\lt H$, does $NhN=h$; with $h\in H$? Or rather some $h'\in H$

The relation was a line in a proof, and I was wondering if it was a typo.

Thanks

Answer 1

$NhN$ has cardinality at least the size of $N$ so this happens iff $N=e$