  We investigate the genera of quotient curves $\mathcal H_q/G$ of the $\mathbb
F_{q^2}$-maximal Hermitian curve $\mathcal H_q$, where $G$ is contained in the
maximal subgroup $\mathcal M_q\leq{\rm Aut}(\mathcal H_q)$ fixing a pole-polar
pair $(P,\ell)$ with respect to the unitary polarity associated with $\mathcal
H_q$. To this aim, a geometric and group-theoretical description of $\mathcal
M_q$ is given. The genera of some other quotients $\mathcal H_q/G$ with
$G\not\leq\mathcal M_q$ are also computed. Thus we obtain new values in the
spectrum of genera of $\mathbb F_{q^2}$-maximal curves. A plane model for
$\mathcal H_q/G$ is obtained when $G$ is cyclic of order $p\cdot d$, with $d$ a
divisor of $q+1$.
