The inner structure of condensed phase domains in monolayers at the air-water interface is studied by Brewster angle microscopy. Condensed phase domains of l-monoglycerides exhibit a 7-fold substructure. Seven segments of different molecular orientation meet at a center. The attention is focused on the orientational relations of the partial lattices separated by a sharp boundary for explaining the observed segment number. The boundary lines of the segments are considered to be along dense lattice rows. Thus a defined change of the molecular orientation occurs at a segment boundary. The interdependence of the lattice parameters and the number of segments is described based on a centered orthorhombic lattice. The geometrical analysis of the inner domain structure shows that the chains are tilted along the bisector of each segment and that the segment boundaries are along next nearest neighbor directions.