The symmetry group of the non-rigid 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) is constructed for the internal rotations of the nitro groups that exhibit low rotation barriers of 5 kcal/mole. The permutation group has 48 operations characterized by the wreath product S-3[S-2]. The nuclear spin statistical weights for TATB with O-17, N-14 and H-1 species are computed and the tunneling splitting patterns of the rotational and rovibronic levels of TATB are constructed for the first time. It is shown that the ground rovibronic state of TATB is split into A(1), A(3), T-1 and T-3 levels. (C) 2004 Elsevier B.V. All rights reserved.