  Fino and Kath determined all possible holonomy groups of seven-dimensional
pseu\-do-Rie\-man\-nian manifolds contained in the exceptional, non-compact,
simple Lie group $\mathrm{G}_2^*$ via the corresponding Lie algebras. They are
distinguished by the dimension of their maximal semi-simple subrepresentation
on the tangent space, the socle. An algebra is called of Type I, II or III if
the socle has dimension 1, 2 or 3 respectively. This article proves that each
possible holonomy group of Type III can indeed be realized by a metric of
signature $(4,3)$. For this purpose, metrics are explicitly constructed, using
Cartan's methods of exterior differential systems, such that the holonomy of
the manifold has the desired properties.
