Hole operations on Hurwitz maps

For a given group G the orientably regular maps with orientation-preserving automorphism are used as vertices of graph O(G), undirected and directed edges showing effect duality hole operations on these maps. Some examples graphs given, including several for small Hurwitz groups. some G, such affine groups AGL1(2e), O(G) is connected, whereas other infinite families, alternating symmetric groups, number connected components unbounded.