  We consider the structure of the plane-line incidence matrix of the
projective space $\mathrm{PG}(3,q)$ with respect to the orbits of planes 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
planes 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 in every plane and planes through
every line are obtained. This corresponds to the numbers of ones in columns and
rows of the submatrices.
