The formation of NaRMn2Ti4O12 compounds (R = rare earth) under high pressure (about 6 GPa) and high temperature (about 1750 K) conditions was studied. Such compounds with R = Sm, Eu, Gd, Dy, Ho, Y adopt an A-site columnar-ordered quadruple-perovskite structure with the generic chemical formula A(2)A'A '' B4O12. Their crystal structures were studied by powder synchrotron X-ray and neutron diffraction between 1.5 and 300 K. They maintain a paraelectric structure with centrosymmetric space group P4(2)/nmc (No. 137) at all temperatures, in comparison with the related CaMnTi2O6 perovskite, in which a ferroelectric transition occurs at 630 K. The centrosymmetric structure was also confirmed by second-harmonic generation. It has a cation distribution of [Na+R3+](A)[Mn2+](A')[Mn2+](A '')[Ti-4(4+)](B)O-12 (to match with the generic chemical formula) with statistical distributions of Na+ and R3+ at the large A site and a strongly split position of Mn2+ at the square-planar A' site. We found a C-type longrange antiferromagnetic structure of Mn2+ ions at the A' and A '' sites below T-N = 12 K for R = Dy and found that the presence of Dy3+ disturbs the long-range ordering of Mn2+ below a second transition at lower temperatures. The first magnetic transition occurs below 8-13 K in all compounds, but the second magnetic transition occurs only for R = Dy, Sm, Eu. All compounds show large dielectric constants of a possible extrinsic origin similar to that of CaCu3Ti4O12. NaRMn2Ti4O12 with R = Er-Lu crystallized in the GdFeO3-type Pnma perovskite structure, and NaRMn2Ti4O12 with R = La, Nd contained two perovskite phases: an AA'(3)B(4)O(12-)type Im (3) over bar phase and a GdFeO3-type Pnma phase.