  If our 3+1-dimensional universe is a brane or domain wall embedded in a
higher dimensional space, then a phenomenon we term the ``clash of symmetries''
provides a new method of breaking some continuous symmetries. A global
$G_{\text{cts}} \otimes G_{\text{discrete}}$ symmetry is spontaneously broken
to $H_{\text{cts}} \otimes H_{\text{discrete}}$, where the continuous subgroup
$H_{\text{cts}}$ can be embedded in several different ways in the parent group
$G_{\text{cts}}$, and $H_{\text{discrete}} < G_{\text{discrete}}$. A certain
class of topological domain wall solutions connect two vacua that are invariant
under {\it differently embedded} $H_{\text{cts}}$ subgroups. There is then
enhanced symmetry breakdown to the intersection of these two subgroups on the
domain wall. This is the ``clash''. In the brane limit, we obtain a
configuration with $H_{\text{cts}}$ symmetries in the bulk but the smaller
intersection symmetry on the brane itself. We illustrate this idea using a
permutation symmetric three-Higgs-triplet toy model exploiting the distinct
$I-$, $U-$ and $V-$spin U(2) subgroups of U(3). The three disconnected portions
of the vacuum manifold can be treated symmetrically through the construction of
a three-fold planar domain wall junction configuration, with our universe at
the nexus. A possible connection with $E_6$ is discussed.
