In-beam nuclear spectroscopic studies of¹⁸²Re, following the reaction¹⁸¹Ta(α, 3n)¹⁸²Re have been made using gamma-ray and internal conversion electron techniques.K-conversion coefficients for several transitions have been measured and the multi-polarities of the various transitions assigned. In particular, the spin and parity of the four-quasi-particle isomeric level at 2256 keV were determined to be 16⁻. Theg-factor of this level has been measured to beg = 0·32 ± 0·05. On the basis of theg-factor and the decay pattern of this level, a configuration {v9/2⁺ [624↑]v7/2⁻ [514↓]v7/2⁻ [503↑]π9/2⁻ [514↑]}_k^x = 16⁻ has been assigned to this level. The nature of the retardation of the gamma transitions deexciting this level is discussed. It is argued that the measured retardation factors can be explained if the nucleus has a triaxial shape.