Normalizer of a subgroup

If $H$ is a {{KNOWL('group.subgroup', 'subgroup')}} of a {{KNOWL('group','group')}} $G$, then the **normalizer** of $H$ is the subgroup \[ N_G(H) = \{ g\in G\mid gHg^{-1} = H\}.\] Equivalently, this is the largest subgroup of $G$ containing $H$ in which $H$ is {{KNOWL('group.subgroup.normal', 'normal')}}.