Single crystals of germanium double salt (NH4)3GeF7 = (NH4)2GeF6·NH4F = (NH4)3[GeF6]F were grown and studied by the methods of polarization optics and X-ray diffraction. The birefringence Δn = (no - ne), the rotation angle of the optical indicatrix ϕ(T) and unit cell parameters were measured in the temperature range 100-400 K. Three structural phase transitions were found at the temperatures: T1↓ = 279.2 K (T1↑ = 279.4 K), T2↑ = 270 K (T2↓ = 268.9 K), T3↓ = 218 K (T3↑ = 227 K). An unusual sequence of symmetry transformations with temperature change was established: P4/mbm (Z = 2) (G1) ↔ Pbam (Z = 4) (G2) ↔ P21/c (Z = 4) (G3) ↔ Pa3[combining macron] (Z = 8) (G4). The crystal structures of different phases were determined. The experimental data were additionally interpreted by a group-theoretical analysis of the complete condensate of order parameters taking into account the critical and noncritical atomic displacements. Strengthening of the N-HF hydrogen bonds can be a driving force of the observed phase transitions.