Hasse diagram of the 8 reflective subgroups of the full octahedral group
Each of the reflective subgroups corresponds to one of the rotational ones, having its Coxeter notation without the plus sign.
But there is no reflective equivalent to [2,3]+ (the symmetric group S3). No subgroup [2,3] exists.

Rotational subgroups
Reflective subgroups
Own work
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