  We show that for certain class of oligomorphic groups there is a version of
multiplication of double cosets in Ismagilov--Olshanski sense. Categories of
(reduced) double cosets are realized as certain categories of partial
bijections. As an example, we consider the ultrahomogeneous linear space
$\mathcal{Z}$ of countable dimension over a finite field equipped with a cubic
form. The group $G$ of automorphisms of $\mathcal{Z}$ is an oligomorphic group,
we describe its open subgroups. According Tsankov, this gives a classification
of its unitary representations. The category of reduced double cosets is the
category of partial linear bijections of finite-dimensional cubic spaces
preserving cubic forms.
