On parallelizable NS-NS backgrounds

We classify non-dilatonic NS-NS type II supergravity backgrounds admitting a consistent absolute parallelism. They are all given by parallelized Lie groups admitting scalar flat bi-invariant Lorentzian metrics. There are seven different classes, some of them containing moduli. For each class we determine the amount of supersymmetry which is preserved: there are examples with 16, 18, 20, 22, 24, 28 and 32 supersymmetries.