Orbits of the stabiliser group of the Segre variety product of three   projective lines
  We prove that the stabiliser group G of the Segre variety product in PG(V) of three projective lines over a field F has four orbits on singular points of PG(V), and that G has five orbits on points of PG(V) if F is finite. 
Michel Lavrauw, John Sheekey
math.CO