The ambient structure and pressure-induced structural changes of a synthetic sodium aluminogermanate with a natrolite (NAT) framework topology (Na−AlGe-NAT) were characterized by using Rietveld refinements of high-resolution synchrotron X-ray powder diffraction data at ambient and high pressures. Unlike a previously established model for Na8Al8Ge12O40·8H2O based on a single-crystal study, the ambient structure of the Na−AlGe-NAT is found to adopt a monoclinic space group Cc (or Fd) with a ca. 6% expanded unit cell. The refined ambient structure of Na8Al8Ge12O40·12H2O indicates an increased water content of 50%, compared to the single-crystal structure. The unit-cell volume and water-content relationships observed between the two Na−AlGe-NAT structures at ambient conditions with 8 and 12 H2O respectively seem to mirror the ones found under hydrostatic pressure between the Na8Al8Si12O40·8H2O and the parantrolite phase Na8Al8Si12O40·12H2O. Under hydrostatic pressures mediated by a pore-penetrating alcohol and water mixture, the monoclinic Na−AlGe-NAT exhibits a gradual decrease of the unit-cell volume up to ca. 2.0 GPa, where the unit-cell volume then contracts abruptly by ca. 4.6%. This is in marked contrast to what is observed in the Na−AlSi-NAT and Na−GaSi-NAT systems, where one observes a pressure-induced hydration and volume expansion due to the auxetic nature of the frameworks. Above 2 GPa, the monoclinic phase of Na−AlGe-NAT transforms into a tetragonal structure with the unit-cell composition of Na8Al8Ge12O40·16H2O, revealing pressure-induced hydration and a unit cell volume contraction. Unlike in the Na−Al,Si-paranatrolite phase, however, the sodium cations in the Na−AlGe-NAT maintain a 6-fold coordination in the monoclinic structure and only become 7-fold coordinated at higher pressures in the tetragonal structure. When comparing the pressure-induced hydration in the observed natrolite-type zeolites, Na−AlGe-NAT appears to have a nonauxetic framework and reveals the highest onset pressure for complete superhydration.