Let $G$ be a group such that:
1) $G$ can be generated by a finite set of elements of infinite order.
2) In $G$ there is a subgroup $H$ such that $H$ is a free group and its index $|G:H|$ in $G$ is finite.
For instance, $G=\left ( \mathbb{Z}/3\mathbb{Z} \right )\ast\left ( \mathbb{Z}/3\mathbb{Z} \right )$ (but $\left ( \mathbb{Z}/2\mathbb{Z} \right )\ast\left ( \mathbb{Z}/2\mathbb{Z} \right )$ does not satisfy the first condition).
Is there any description of such type of groups?