In this talk I describe some special families of K3-surfaces with Picard number 19. The surfaces are obtained as the minimal resolutions of quotients X/G , where G is a finite subgroup of SO(4,R) and X denotes a G-invariant surface in P₃(C).

      I describe the Neron-Severi group, and I show that it contains some divisible classes. These classes correspond to cyclic coverings, which establish some relations between these families of K3-surfaces. Finally with the help of lattice theory and the theory of quadratic forms I compute the transcendental lattices of the K3-surfaces.