  An extended Kleinian group whose orientation-preserving half is a Schottky
group is called an extended Schottky group. These groups correspond to the real
points in the Schottky space. Their geometric structures is well known and it
permits to provide information on the locus of fixed points of symmetries of
handlebodies. A group generated by two different extended Schottky groups, both
with the same orientation-preserving half, is called a dihedral extended
Schottky group. We provide a structural description of these type of groups
and, as a consequence, we obtain sharp upper bounds for the sum of the
cardinalities of the connected components of the locus of fixed points of two
or three different symmetries of a handlebody.
