The low-lying structure of 188,190,192 W has been studied following β decays of the neutron-rich mother nuclei 188,190,192 Ta produced following the projectile fragmentation of a 1-GeV-per-nucleon 208 Pb primary beam on a natural beryllium target at the GSI Fragment Separator. The β-decay half-lives of 188 Ta, 190 Ta, and 192 Ta have been measured, with γ -ray decays of low-lying states in their respective W daughter nuclei, using heavy-ion β-γ correlations and a position-sensitive silicon detector setup. The data provide information on the low-lying excited states in 188 W, 190 W, and 192 W, which highlight a change in nuclear shape at 190 W compared with that of lighter W isotopes. This evolution of ground-state structure along the W isotopic chain is discussed as evidence for a possible proton subshell effect for the A ∼ 190 region and is consistent with maximization of the γ -softness of the nuclear potential around N ∼ 116.