  We consider the structure of the point-line incidence matrix of the
projective space $\mathrm{PG}(3,q)$ connected with orbits of points and lines
under the stabilizer group of the twisted cubic. Structures of submatrices with
incidences between a union of line orbits and an orbit of points are
investigated. For the unions consisting of two or three line orbits, the
original submatrices are split into new ones, in which the incidences are also
considered. For each submatrix (apart from the ones corresponding to a special
type of lines), the numbers of lines through every point and of points lying in
every line are obtained. This corresponds to the numbers of ones in columns and
rows of the submatrices.
