We suggest a new general method for counting conjugacy classes of subgroups in an arbitrary  finitely generated group. Explicite formulae for the number of conjugacy classes will be obtained. As a consequence we give a short prove of the results by Valery Liskovets,  Galina Pozdnyakova and the author on the number of non-equivalent coverings over compact Riemann surface. Some more application are recent results on the number of unrooted maps  with prescribed number of edges on a closed suface of a given genus.

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