Monodromy groups of product type

The combination of this paper and its companion complete the classification of monodromy groups of indecomposable coverings of complex curves $f:X\to {\mathbb{P}}^1$ of sufficiently large degree in comparison to the genus of $X$. In this paper we determine all such coverings with monodromy group $G\le S_{\mathrm{\ell }}\wr S_t$ of product type for $t\ge 2$.