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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 algebrainvariant under Cartan automorphism. We obtain that $\mathbb Z_2$ monopoles inthis theory belong to different classes of $su(2)$ embeddings associated tocontinuous families of up to four parameters. This result generalizes thediscrete families of $\mathbb Z_2$ monopoles previously known as well as itshows new classes of embeddings.

Continuous families of Z(2) monopoles in SU(4) Yang-Mills-Higgs theory