  We study the anomalous Hall effect on the antiferromagnetic
coloring-triangular lattice with a coplanar magnetic configuration in presence
of a spin-orbit interaction. The effect of the spin-orbit coupling is included
at effective level as a rotation of the electronic spin as the electrons hop
from site to site. Our result reveals that a finite Hall conductivity in the
planar 120$^{\circ}$ structure takes place if a finite spin-orbit coupling is
present. A quantized Hall conductivity occurs at global band gaps resulting
from the topologically non-trivial band structure.
