Some remarks on Bianchi type-II, VIII and IX models
  Within the scope of anisotropic non-diagonal Bianchi type-II, VIII and IX spacetime it is shown that the off-diagonal components of the corresponding metric impose severe restrictions on the components of the energy momentum tensor in general. If the energy momentum tensor is considered to be diagonal one, the spacetime, expect a partial case of BII, becomes locally rotationally symmetric. 
Bijan Saha
gr-qc