In this paper we study the following problem. Given an NEC group F and the dihedral group Dp, with p a prime, how many non conjugate normal subgroups of F has Dp as quotient group? This is equivalent to asking how many non-biconformally equivalent Klein surfaces that are coverings of the orbifold whose fundamental group is F admit Dp as a group of automorphisms. A related question is the classification of actions of Dp on a Riemann surface. Natanzon [9] gives a classification for D2-actions on Riemann surfaces. This paper is a generalization to NEC groups of the paper of Lloyd [6].
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