  The intrinsic spin Hall conductance shows rich sign changes by applying a
perpendicular magnetic field in a two-dimensional hole gas. Especially, a
notable sign changes can be achieved by adjusting the characteristic length of
the Rashba coupling and hole density at moderate magnetic fields. This sign
issue may be easily realized in experiments. The oscillations of the intrinsic
spin Hall conductance as a function of 1/$B$ is nothing else but Shubnikov-de
Haas oscillations, and the additional beatings can be quantitatively related to
the value of the spin-orbit coupling parameter. The Zeeman splitting is too
small to introduce effective degeneracy between different Landau levels in a
two-dimensional hole gas, and the resonant intrinsic spin Hall conductance
appears in high hole density and strong magnetic field due to the transition
between mostly spin-$-{1/2}$ holes and spin-3/2 holes is confirmed. Two likely
ways to establish intrinsic spin Hall effect in experiments and a possible
application are suggested.
