  Given a symmetry $\tau$ of a closed Riemann surface $S$, there exists an
extended Kleinian group $K$, whose orientation-preserving half is a Schottky
group $\Gamma$ uniformizing $S$, such that $K/\Gamma$ induces $\langle \tau
\rangle$; the group $K$ is called an extended Schottky group. A geometrical
structural description, in terms of the Klein-Maskit combination theorems, of
both Schottky and extended Schottky groups is well known. A dihedral extended
Schottky group is a group generated by the elements of two different extended
Schottky groups, both with the same orientation-preserving half. Such
configuration of groups corresponds to closed Riemann surfaces together with
two different symmetries and the aim of this paper is to provide a geometrical
structure of them. This result can be used in study of three dimensional
manifolds and as an illustration we give the sharp upper bounds for the total
number of connected components of the locus of fixed points of two and three
different symmetries of a handlebody with a Schottky structure.

Geometric Topology