Recent experimental data on the low-lying states in W-190 show a change in the E(4(1)(+))/E(2(1)(+)) behavior compared to less neutron-rich neigbors. Self-consistent axially-deformed Hartree-Fock calculations, using a separable monopole interaction, of nuclei in the vicinity of W-190 are performed to systematically examine the evolution of ground state quadrupole deformations. It is found that the neutron number N=116 causes a coexistence of oblate and prolate shapes, with a weak dependence on proton number, thereby hindering the development of these isotones as well-deformed rotors.