  If $(G_1, G_2)$ is a dual reductive pair of type I in $Sp(W)$, it is known
that the degree $8$ metaplectic cover of $Sp(W)$ splits over $G_1G_2$, with one
obvious exception. In this paper we replace $G_1G_2$ by a larger subgroup
obtained via similitude groups, and show that the degree $8$ metaplectic cover
splits, with the same obvious exception.
