Does N/H=K/H under some terms mean N=K?

Let $G$ be a group and let $K$ be a normal subgroup of $G.$ Now let $H$ and $N$ be normal subgroups of $G$ containing $K.$ Given $N/K=H/K$ can I show $N=H$ necessarily? Is there a way?

• The assumption is that they are the same group. – Meitar Jan 10 '15 at 14:14

If $H/K = N/K$, then $N=H$ by the correspondence theorem: there is a bijection between the subgroups of $G$ containing $K$ and the subgroups of $G/K$