  The list of six previously known nontrivial stationary points in the scalar
potential of N=8, D=4 supergravity with gauge group SO(8) is extended by
fourteen new entries, whose properties have been obtained numerically using the
sensitivity backpropagation technique. Eight of the new solutions break the
gauge group completely, while three have a residual symmetry of U(1). Three
further ones break the gauge group to U(1)xU(1), and while the approximate
numerical data are somewhat inconclusive, there is evidence that one of these
may have a residual N=1 supersymmetry, hence correspond to a stable vacuum. It
must be pointed out that this list of new solutions most likely is not
exhaustive.
