We classify irreducible II_1 subfactors A \subset B such that B \ominus A is reducible as an A-A bimodule, with index at most 6+1/5, leaving aside the composite subfactors at index exactly 6. Previous work has already achieved this up to index 3+\sqrt{ 5} \approx 5.23. We find there are exactly three such subfactors with index in (3+\sqrt{ 5}, 6+1/5], all with index 3+2\sqrt{ 2}. One of these comes from SO(3)_q at a root of unity, while the other two appear to be closely related, and are `braided up to a sign'.
Categories: math.OA math.QA