Let $G$ be any countable discrete group, and $H_1, H_2$ be two subgroups of $G$ with some fixed finite index $m>1$.
My question is:
Is it always possible to find some automorphism $\phi$ of $G$, i.e., $\phi\in Aut(G)$, such that $\phi(H_1)=H_2$?
If not, could any one give some counterexample to illustrate this? Thanks in advance!