  We study the duality between M-theory on compact holonomy G2-manifolds and
the heterotic string on Calabi-Yau three-folds. The duality is studied for
K3-fibered G2-manifolds, called twisted connected sums, which lend themselves
to an application of fiber-wise M-theory/Heterotic Duality. For a large class
of such G2-manifolds we are able to identify the dual heterotic as well as
F-theory realizations. First we establish this chain of dualities for smooth
G2-manifolds. This has a natural generalization to situations with non-abelian
gauge groups, which correspond to singular G2-manifolds, where each of the
K3-fibers degenerates. We argue for their existence through the chain of
dualities, supported by non-trivial checks of the spectra. The corresponding 4d
gauge groups can be both Higgsable and non-Higgsable, and we provide several
explicit examples of the general construction.
