Statement:
Let H be a subgroup of a group G. N(H) = $\{x \in G | xHx^{-1} = H\}$, the normalizer of H and C(H)= $\{x \in G|xhx^{-1} = h \hspace{5mm}\forall h \in G \}$
Then $N(H)/C(H) \cong$ to a subgroup of $Aut(H)$.
I am aware of the textbook proof. But I am unbale to understand it in an intuitive sense. Especially the way they use this as a counting tool. Like in this question ,
Group of order $255$ is cyclic
Some non trivial but simple examples which help showcase the usefulness of the theorem would be helpful.
