In this paper, we discuss an approach in arriving at a torsion free subgroup of p32 - the group of orientation preserving isometries in a triangle group *p32, using color symmetries of its related tiling. We also present the relation that exists between torsion free subgroups of p32 and precise colorings of a 3^p tiling. A group is said to be torsion free if all its nonidentity elements are of infinite order.