  It is well known that the collection of uniformizations of a closed Riemann
surface $S$ is partially ordered; the lowest ones are the Schottky
unformizations, that is, tuples $(\Omega,\Gamma,P:\Omega \to S)$, where
$\Gamma$ is a Schottky group with region of discontinuity $\Omega$ and
$P:\Omega \to S$ is a regular holomorphic cover map with $\Gamma$ as its deck
group.
  Let $\tau:S \to S$ be a conformal (respectively, anticonformal) automorphism
of $S$ of finite order $n$, and let $(\Omega,\Gamma,P:\Omega \to S)$ be a
Schottky uniformization of $S$. Assume that $\tau$ lifts with respect to the
previous Schottky uniformization, that is, there exists a M\"obius
(respectively, extended M\"obius) transformation $\kappa$, keeping $\Omega$
invariant, with $P \circ \kappa=\tau \circ P$. The Kleinian (respectively,
extended Kleinian) group $K=< \Gamma, \kappa >$ contains $\Gamma$ as a finite
index normal subgroup and $K/\Gamma \cong {\mathbb Z}_{n}$. We provide a
structural picture of $K$ in terms of the Klein-Maskit's combination theorems
and some basic groups. Some consequences are (i) the determination of the
number of topologically different types of such groups (fixed $n$ and the rank
of the Schottky normal subgroup) and (ii) for $n$ prime, the number of normal
Schottky normal subgroups, up to conjugacy, that $K$ has.
