γ -ray transitions between low-spin states of the neutron-rich 84,86,88 Ge were measured by means of in-flight γ -ray spectroscopy at 270 MeV/u. Excited 6 + 1 , 4 + 1,2 , and 2 + 1,2 states of 84,86 Ge and 4 + 1 and 2 + 1,2 states of 88 Ge were observed. Furthermore, a candidate for a 3 + 1 state of 86 Ge was identified. This state plays a key role in the discussion of ground-state triaxiality of 86 Ge, along with other features of its low-energy level scheme. A new region of triaxially deformed nuclei is proposed in the Ge isotopic chain.