Methods of the structure analysis were used to determine the incommensurate structure modulation in a sample of hauyne from Laacher Lake, Germany. The modulation parameter n=0.145, determined using single-crystal patterns, was refined using powder data. An indexing technique for additional reflections (satellites) using a parameter subcell and Miller index main reflections was suggested. Crystallographic characteristics of the hauyne of Laacher Lake are compared with that of hauyne from Sacrafano (Italy) and with lazurtes from Baikal, Pamir, and Afghanistan. We found that the crystal structure modulation can serve as a source of paragenesis information on sulphate bearing sodalte group minerals.