Going through the archives I found a message from Mike Reid, dated
August 20, where he investigates the filtration through different
subgroups. I missed the original, but he says:
> winter's filtration is 56 --> 49 --> kl --> 1. it may be the case that
> this can be improved by replacing kl with 17 , and allowing all face
> turns available in the subgroup 49. i haven't had the time to look into
> this yet.
For the record, the filtration is from Herbert Kociemba, and it is:
56 --> 49 --> 1.
So there is no intermediate stage between 49 and 1.