Accidental degeneracies and symmetry groups

It is usually assumed that the appearance of accidental degeneracy in the energy levels of a given Hamiltonian is due to a symmetry group. By considering the elementary problem of a rotator with spin-orbit coupling, when the strength of the latter is equal to the inverse of the moment of inertia, we find that this assumption does not explain the degeneracy of all the levels of the Hamiltonian. Thus the relation between accidental degeneracies and symmetry group merits further probing.