  We consider an SU(4) Yang-Mills-Higgs theory spontaneously broken to $SO(4)$
by a scalar field in the $n\times n$ representation and the unbroken algebra
invariant under Cartan automorphism. We obtain that $\mathbb Z_2$ monopoles in
this theory belong to different classes of $su(2)$ embeddings associated to
continuous families of up to four parameters. This result generalizes the
discrete families of $\mathbb Z_2$ monopoles previously known as well as it
shows new classes of embeddings.
