  We study the spin Hall effect in the kagom\'{e} lattice with Rashba
spin-orbit coupling. The conserved spin Hall conductance $\sigma_{xy}^{s}$ (see
text) and its two components, i.e., the conventional term $\sigma_{xy}^{s0}$
and the spin-torque-dipole term $\sigma_{xy}^{s\tau}$, are numerically
calculated, which show a series of plateaus as a function of the electron Fermi
energy $\epsilon_{F}$. A consistent two-band analysis, as well as a Berry-phase
interpretation, is also given. We show that these plateaus are a consequence of
the various Fermi-surface topologies when tuning $\epsilon_{F}$. In particular,
we predict that compared to the case with the Fermi surface encircling the
$\mathbf{\Gamma}$ point in the Brillouin zone, the amplitude of the spin Hall
conductance with the Fermi surface encircling the $\mathbf{K}$ points is twice
enhanced, which makes it highly meaningful in the future to systematically
carry out studies of the $\mathbf{K}$-valley spintronics.
