  Motivated by an analogous result for K3 models, we classify all groups of
symmetries of non-linear sigma models on a torus T^4 that preserve the N=(4,4)
superconformal algebra. The resulting symmetry groups are isomorphic to certain
subgroups of the Weyl group of E8, that plays a role similar to the Conway
group for the case of K3 models. Our analysis heavily relies on the triality
automorphism of the T-duality group SO(4,4,Z). As a byproduct of our results,
we discover new explicit descriptions of K3 models as asymmetric orbifolds of
torus CFTs.
