Denote $F_2=\langle a, b\rangle$ to be the free group on two generators $a, b$.

Let $H\leq F_2$ to be a subgroup with finite index $n$, so $H\cong F_{n+1}$ by Nielsen–Schreier theorem, recall that $H$ is called self-normalizing if the normalizer of $H$ inside $F_2$ to equal to $H$,

Question:

Can anyone give me a subgroup $H\leq F_2$ with finite index and self-normalizing?

Note that $\langle a\rangle$ is a normalizing subgroup but with infinite index. Also $n$ should be odd.