  We solve a problem posed by Cardinali and Sastry [2] about factorization of
$2$-covers of finite classical generalized quadrangles. To that end, we develop
a general theory of cover factorization for generalized quadrangles, and in
particular we study the isomorphism problem for such covers and associated
geometries. As a byproduct, we obtain new results about semipartial geometries
coming from $\theta$-covers, and consider related problems.

Combinatorics