  The classical phase diagram of the Kane-Mele-Heisenberg model is obtained by
three complementary methods: Luttinger-Tisza, variational minimization, and the
iterative minimization method. Six distinct phases were obtained in the space
of the couplings. Three phases are commensurate with long-range ordering,
planar N{\'e}el states in horizontal plane (phase.I), planar states in the
plane vertical to the horizontal plane (phase.VI) and collinear states normal
to the horizontal plane (phase.II). However the other three, are infinitely
degenerate due to the frustrating competition between the couplings, and
characterized by a manifold of incommensurate wave-vectors. These phases are,
planar helical states in horizontal plane (phase.III), planar helical states in
a vertical plane (phase.IV) and non-coplanar states (phase.V). Employing the
linear spin-wave analysis, it is found that the quantum fluctuations select a
set of symmetrically equivalent states in phase.III, through the quantum
order-by-disorder mechanism. Based on some heuristic arguments is argued that
the same scenario may also occur in the other two frustrated phases VI and V.
