  We generalize the "facial weak order" of a finite Coxeter group to a partial
order on a set of intervals in a complete lattice. We apply our construction to
the lattice of torsion classes of a finite-dimensional algebra and consider its
restriction to intervals coming from stability conditions. We give two
additional interpretations of the resulting "facial semistable order": one
using cover relations, and one using Bongartz completions of 2-term presilting
objects. For $\tau$-tilting finite algebras, this allows us to prove that the
facial semistable order is a semidistributive lattice. We then show that, in
any abelian length category, our new partial order can be partitioned into a
set of completely semidistributive lattices, one of which is the original
lattice of torsion classes.
