  We show that every non-decreasing function $f\colon \mathbb N\to \mathbb N$
bounded from above by $a^n$ for some $a\ge 1$ can be realized (up to a natural
equivalence) as the conjugacy growth function of a finitely generated group. We
also construct a finitely generated group $G$ and a subgroup $H\le G$ of index
2 such that $H$ has only 2 conjugacy classes while the conjugacy growth of $G$
is exponential. In particular, conjugacy growth is not a quasi-isometry
invariant.
