The website of the Saxifraga Society had lots of good information - but is no longter available.
https://www.saxifraga.org I am aware of this list of saxifraga Sections and subsections, abbreviated as follows:
AIZ subsection Aizoonia;
CIL section Ciliatae;
COT section Cotylea;
CLN subsection Cuneifoliatae;
CYM section Cymbalaria;
ENG subsection Engleria;
FLO subsection Florulentae;
GYM section Gymnopera;
HET section Heterisia;
HOL subsection Holophyllae;
IRR section Irregulares;
KAB subsection Kabschia;
MER section Merkianae;
MES section Mesogyne;
MIC subsection Micranthes;
MUT subsection Mutatae;
ODO section Odontophyllae;
OPP subsection Oppositifoliae;
ROT subsection Rotundifoliatae;
SAX subsection Saxifraga;
STE subsection Stellares;
TRA section Trachyphyllum;
TRD subsection Tridactylites;
TRP subsection Triplinervium;
XAN section Xanthizoon.
..... but I confess I don't know about the group names you mention.
Sorry!