  We exhibit examples of closed Riemannian 7-manifolds with holonomy G_2 such
that the underlying manifolds are diffeomorphic but whose associated
G_2-structures are not homotopic. This is achieved by defining two invariants
of certain U(3)-structures. We show that these agree with the invariants of
G_2-structures defined by Crowley and Nordstr\"om. We construct a suitable
coboundary for G_2 manifolds obtained via the Twisted Connected Sum method that
allows the invariants to be computed in terms of the input data of the
construction. We find explicit examples where the invariants detect different
connected components of the moduli of G_2-metrics.
