On the genera of subfields of the Hermitian function field (Q596579)

\textit{A.~Garcia, H.~Stichtenoth} and \textit{C.~Xing} [Compos. Math. 120, No. 2, 137--170 (2000; Zbl 0990.11040)] constructed a large number of maximal curves over \({\mathbb F}_{q^2}\) by considering the fixed fields of certain groups of automorphisms of the Hermitian function field \(H\). The authors extend some of the results of Garcia-Stichtenoth-Xing and produce additional subgroups of the automorphism group of \(H\). In this way, the authors find new values of \(g\) for which a maximal curve of genus \(g\) exists over \({\mathbb F}_{q^2}\).