  We classify the orbits of elements of the tensor product spaces
${\mathbb{F}}^2\otimes {\mathbb{F}}^3 \otimes {\mathbb{F}}^3$ for all finite;
real; and algebraically closed fields under the action of two natural groups.
The result can also be interpreted as the classification of the orbits in the
$17$-dimensional projective space of the Segre variety product of a projective
line and two projective planes. This extends the classification of the orbits
in the $7$-dimensional projective space of the Segre variety product of three
projective lines [M. Lavrauw and J. Sheekey: Orbits of the stabiliser group of
the Segre variety product of three projective lines, Finite Fields Appl.
(2014)]. The proof is geometric in nature, relies on properties of the Segre
embedding, and uses the terminology of projective spaces.
