On the spectrum of genera of quotients of the Hermitian curve

We investigate the genera of quotient curves ${\mathcal{H}}_q\mathrm{/}G$ of the $\mathbb F_{q^2}$-maximalHermitiancurve$\mathcal H_q$,where$G$ is contained in the maximal subgroup ${\mathcal{M}}_q\le \mathrm{A}\mathrm{u}\mathrm{t}({\mathcal{H}}_q)$ fixing a pole-polar pair $(P,\mathrm{\ell })$ with respect to the unitary polarity associated with $\mathcal H_q$\mathrm{.}Tothisaim,ageometricandgroup-theoreticaldescriptionof$\mathcal M_q$isgiven\mathrm{.}Thegeneraofsomeotherquotients$\mathcal H_q/G$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 ${\mathcal{H}}_q\mathrm{/}G$ is obtained when $G$ is cyclic of order $p\cdot d$, with $d$ a divisor of $q+1$.