  A local SL(2,Z) transformation on the Type IIB brane configuration gives rise
to an interesting class of superconformal field theories, known as the S-fold
CFTs. Previously it has been proposed that the corresponding quiver theory has
a link involving the T(U(N)) theory. In this paper, we generalise the preceding
result by studying quivers that contain a T(G) link, where G is self-dual under
S-duality. In particular, the cases of G = SO(2N), USp'(2N) and G_2 are
examined in detail. We propose the theories that arise from an appropriate
insertion of an S-fold into a brane system, in the presence of an orientifold
threeplane or an orientifold fiveplane. By analysing the moduli spaces, we test
such a proposal against its S-dual configuration using mirror symmetry. The
case of G_2 corresponds to a novel class of quivers, whose brane construction
is not available. We present several mirror pairs, containing G_2 gauge groups,
that have not been discussed before in the literature.
