We analyze the classical stable configurations of an extra-dimensional gauge theory, in which the extra dimensions are compactified on a torus. Depending on the particular choice of gauge group and the number of extra dimensions, the classical vacua compatible with four-dimensional Poincaré invariance and zero instanton number may have zero energy. For SU(N) on a two-dimensional torus, we find all possible degenerate zero-energy stable configurations in terms of continuous or discrete and continous parameters, for the case of trivial or non-trivial 't Hooft non-abelian flux, respectively. For the latter, an interesting rank-lowering symmetry breaking mechanism follows, in contrast to the usual Scherk-Schwarz mechanism with trivial 't Hooft flux. We explicitely describe the residual symmetries of each vacua.