Subgroups in $G$ of the form $gHg^{-1}$

Question

Let $G$ be a group and $H$ be a subgroup of finite index. Prove that there is only a finite number of distinct subgroups in $G$ of the form $gHg^{-1}$ where $g$ belongs to $G$.

Answer 1

HINT: If $g'\in gH$, what can you say about $g'H(g')^{-1}$?