Considering a closed orientable surface as a configuration space in robotics or a real moment-angle complex in toric topology, it is seen that  acts on it. Restricting also to four typical proper subgroups, there are five orbit spaces. Their homology groups are known for proper subgroup cases. But the final case is difficult and left unknown. The purpose of this paper is to solve this case completely. In addition, we summarize the results for all cases.

homology, orbifold, dihedral group.