In this paper, we consider hyperbolic rotation (G0), hyperbolic translation (G1) and horocyclic rotation (G2) groups in H3, which is called Minkowski model of hyperbolic space. Then, we investigate extrinsic differential geometry of invariant surfaces under subgroups of G0 in H3. Also, we give explicit parametrization of this invariant surfaces with respect to constant hyperbolic curvature of p...