  Bifurcation with symmetry is considered in the case of an isotropy subgroup
with a two-dimensional fixed point subspace and non-zero quadratic terms. In
general, there are one or three branches of solutions, and five qualitatively
different phase portraits, provided that two non-degeneracy conditions are
satisfied. Conditions are also derived to determine which of the five possible
phase portraits occurs, given the coefficients of the quadratic terms. The
results are applied to the problem of bifurcation with spherical symmetry,
where there are six irreducible representations for which the subspace of
solutions with cubic symmetry is two-dimensional. In each case, the number of
solutions and their stability is found.
