The/~ decay of the longer-lived isomer in l~176 has been studied at the fission-product separator JOSEF. Measurements of 7-ray singles spectra, of 7-7 coincidences and of 7-7 angular correlations have been performed. A value of tl/2 = 2.99(11)s has been determined for the isomer which probably has U= 4 + or 5 +. A scheme of the levels of l~176 which are populated in the decay of this isomer has been established. Information on the spins of several states of l~176 has been obtained. Thus, I=0 levels have been identified at 1,505, 2,038 and 2,087 keV. The mixing ratios have been determined for the 23 ~2~ and 2~---+2~ transitions. The results provide evidence for a vibrational structure of X~176 with separate bands based on the ground state and on the first excited 0 + level.