  A vector space partition $\mathcal{P}$ of the projective space
$\operatorname{PG}(v-1,q)$ is a set of subspaces in $\operatorname{PG}(v-1,q)$
which partitions the set of points. We say that a vector space partition
$\mathcal{P}$ has type $(v-1)^{m_{v-1}} \dots 2^{m_2}1^{m_1}$ if precisely
$m_i$ of its elements have dimension $i$, where $1\le i\le v-1$. Here we
determine all possible types of vector space partitions in
$\operatorname{PG}(7,2)$.
