  We examine the prediction of supersymmetric quantum mechanics that bands with
identical gamma-ray energies occur in quartets. The experimental data suggest
that this scenario is actually realized in nature. In the $A=150$ mass region,
four known pairs of isospectral bands can be grouped in two quartets, while
there are indications of such patterns around $A=190$. We introduce a small
supersymmetry breaking, necessary to describe the details of the data. We
derive relations among the transition rates that can be used to test our
predictions. pacs: 21.10.Re, 11.30.Pb, 21.60.Fw, 23.20.Lv
