Six new zirconogermanates have been prepared under hydrothermal conditions using amines as bases. There are four new structure types (ASU-n) with a common motif of ZrGe5. ASU-23 is a layered structure: ZrGe3O8(OH)F.[C10H26N4].H2O, space group P2(1)/n, a = 6.7957(8) Angstrom, b = 12.700(1) Angstrom, c = 24.293(3) Angstrom, beta = 97.936(2)degrees, V = 2076.4(4) Angstrom(3). ASU-24 is a pillared layered structure: Zr3Ge6O18(OH2,F)(4)F-2.[C6H18N2](2).[C6H17N2](2).2H(2)O, space group P2(1)/n, a = 7.4249(3) Angstrom, b = 25.198(1) Angstrom, c = 11.3483(5) Angstrom, beta = 90.995(1)degrees, V = 2122.9(2) Angstrom(3). This material has the lowest framework density (FD) of any oxide material that we are aware of (FD = 8.48 metal atoms/nm(3)). Two other materials form three-dimensional open-frameworks, ASU-25: ZrGe3O9.[C3H12N2], space group P112(1)/a, a = 13.1994(4) Angstrom, b = 7.6828(2) Angstrom, c = 11.2373(3) Angstrom, gamma = 91.233(3)degrees, V = 1139.29(5) Angstrom(3). The other is ASU-26: ZrGe3O9.[C2H10N2], space group Pn, a = 13.7611(3) Angstrom, b = 7.7294(2) Angstrom, c = 11.2331(3) Angstrom, beta = 104.793(1)degrees, V = 1155.21(4) Angstrom(3). ASU-25 is related to the mineral umbite K2ZrSi3O9.H2O. The germanium equivalent has been prepared through the inorganic route: K2ZrGe3O9.H2O, space group P2(1)2(1)2(1), a = 13.6432(6) Angstrom, b = 7.4256(3) Angstrom, c = 10.3973(4) Angstrom, V = 1053.33(8) Angstrom(3). The structural relationships between ASU-25 and its inorganic counterpart are described. The thermal decomposition of the germanium umbite generated the cyclic trigermanate K2ZrGe3O9, analogue of the mineral wadeite, crystallizing in the orthorhombic system, a = 7.076 Angstrom, b = 12.123 Angstrom, c = 10.451 Angstrom, V = 904.5 Angstrom(3).