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Following up on an earlier thread I have explored the UFR/UF coset space. The number of UF cosets in the UFR group is given by:

The first three factors are the number of ways the corner cubie position and the two edge cubie positions which are not on the UF faces may be configured. The factor of 6 is for the corner position permutation. Of the 720 corner position permutations on the UF faces achievable using the UFR face turns only 120 are achievable using the UF face turns. Thus the corner permutation may be one of six cosets. The flip of the seven UF edge cubies is constrained under the UF face turns, one cannot perform a double edge flip in this group. This gives rise to a factor of two to the sixth for the edge flip (flip parity determines the flip of the seventh edge cubie). As Bruce Norskrog pointed out in the earlier thread, the above number is the same as the order of the UFR group divided by the order of the UF group, so things check out.