  The 6d $(2,0)$ theory has codimension-one symmetry defects associated to the
outer-automorphism group of the underlying ADE Lie algebra. These symmetry
defects give rise to twisted sectors of codimension-two defects that are either
regular or irregular corresponding to simple or higher order poles of the Higgs
field. In this paper, we perform a systematic study of twisted irregular
codimension-two defects generalizing our earlier work in the untwisted case. In
a class S setup, such twisted defects engineer 4d ${\mathcal N}=2$
superconformal field theories of the Argyres-Douglas type whose flavor
symmetries are (subgroups of) non-simply-laced Lie groups. We propose formulae
for the conformal and flavor central charges of these twisted theories,
accompanied by nontrivial consistency checks. We also identify the 2d chiral
algebra (vertex operator algebra) of a subclass of these theories and determine
their Higgs branch moduli space from the associated variety of the chiral
algebra.
