  A well known class of objects in combinatorial design theory are {group
divisible designs}. Here, we introduce the $q$-analogs of group divisible
designs. It turns out that there are interesting connections to scattered
subspaces, $q$-Steiner systems, design packings and $q^r$-divisible projective
sets.
  We give necessary conditions for the existence of $q$-analogs of group
divsible designs, construct an infinite series of examples, and provide further
existence results with the help of a computer search.
  One example is a $(6,3,2,2)_2$ group divisible design over
$\operatorname{GF}(2)$ which is a design packing consisting of $180$ blocks
that such every $2$-dimensional subspace in $\operatorname{GF}(2)^6$ is covered
at most twice.
