Consider the adjoint representation $Ad:G\rightarrow Aut({\frak g})$ for the Lie group $G$ and its Lie algebra $\frak g$. Let $H$ be a closed connected subgroup of $G$.
How to show that $\{g\in G; Ad_g({\frak h})={\frak h}\}$ is the $N_G(H)$ (i.e the normalizer of $H$ in $G$)?