Subgroups — C₇⋊C₉×C₃₈₉ #37587739

Order 24507.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₃₈₉	C₃	1	1	yes	maximal, characteristic
2	C₉×C₃₈₉	—	7	1	no	maximal, Hall
3	C₇×C₃₈₉	C₉	1	1	yes	characteristic, complemented, Hall
4	C₃×C₃₈₉	ΓL(1,𝔽₈)	1	1	yes	characteristic
5	C₃₈₉	C₇⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
6	C₇⋊C₉	C₃₈₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₇	C₃×C₃₈₉	1	1	yes	characteristic
8	C₉	—	7	1	no	Sylow
9	C₇	C₉×C₃₈₉	1	1	yes	characteristic, complemented, Sylow
10	C₃	ΓL(1,𝔽₈)×C₃₈₉	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.