Q) If H is of finite index in G prove that there exists a subgroup N of G contained in H, and of finite index in G such that $\displaystyle aNa^{-1} = N $ .

In a previous problem, I proved that if H is a subgroup of G, then $\displaystyle N = \bigcap xHx^{-1} $ is a subgroup of G such that $\displaystyle aNa^{-1} = N $. So I'm assuming that this is the same subgroup that is being talked about in the above question. How do I prove that it has finite index?