The spectrum of baryons containing heavy quarks of one flavor is described in terms of representations of the group SU(2){times}SU(6), where the two factor groups refer to spin rotations of the heavy quarks and spin-flavor rotations of the light quarks, respectively. This symmetry has a natural interpretation in the heavy quark limit. We exhibit the decomposition of baryon mass operators under this symmetry and compare to experimental results. We discuss the relation of this analysis to that of large-{ital N}{sub {ital c}} QCD as well as four-flavor SU(8), and indicate the generalization of this work to other properties of heavy baryons. {copyright} {ital 1996 The American Physical Society.}