6 6 3 ## The LS6 with transitive autotopism group. The first 2 are groups
abcdef
badcfe
cdefab
dcfeba
efabcd
febadc

abcdef
badcfe
ceafbd
dfbeac
ecfadb
fdebca

abcdef
bcaefd
cabfde
dfebac
edfcba
fedacb