# Let $H$ be a subgroup of $G$. $S=\{g\in G\mid ghg^{-1}\in H\}$. Is $S= N_{G(H)}$? [duplicate]

Let $$H$$ be a subgroup of $$G$$.

$$S=\{g\in G\mid ghg^{-1}\in H,\forall h\in H\}$$.

I know that $$N_G(H)\subset S$$. But I can't seem to find any counterexamples for the other inclusion. Any ideas?