A K{sup {pi}}=13{sup +}, 280 ns four-quasiparticle isomer in the odd-odd nucleus {sup 174}Lu has been identified and characterized. The isomer decays to both K{sup {pi}}=7{sup +} and K{sup {pi}}=0{sup +} rotational bands obtained from the parallel and antiparallel coupling of the proton 7/2{sup +}[404] and neutron 7/2{sup +}[633] orbitals. K mixing caused by particle-rotation coupling explains the anomalously fast transition rates to the 7{sup +} band but those to the 0{sup +} band are caused by a chance degeneracy between the isomer and a collective state, allowing the mixing matrix element for a large K difference to be deduced.