Let $X$ be a subgroup of a Coxeter group $W$. In , the authors developed the notion of $X$-posets, which are defined on certain equivalence classes of the (right) cosets of $X$ in $W$. These posets can be thought of as a generalization of the well-known Bruhat order of $W$. This article provides a catalogue of all the $X$-posets for various small Coxeter groups.
"$X$-POSETS OF CERTAIN COXETER GROUPS." Taiwanese J. Math. 17 (6) 1901 - 1919, 2013. https://doi.org/10.11650/tjm.17.2013.3263