  Energies for excited isospin I=1/2 and I=3/2 states that include the nucleon
and Delta families of baryons are computed using quenched, anisotropic
lattices. Baryon interpolating field operators that are used include nonlocal
operators that provide G_2 irreducible representations of the octahedral group.
The decomposition of spin 5/2 or higher spin states is realized for the first
time in a lattice QCD calculation. We observe patterns of degenerate energies
in the irreducible representations of the octahedral group that correspond to
the subduction of the continuum spin 5/2 or higher. The overall pattern of
low-lying excited states corresponds well to the pattern of physical states
subduced to the irreducible representations of the octahedral group.
