Subgroups — C₉×C₄₇×C₈₉ #49178917

Order 37647.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₇×C₈₉	C₃	1	1	yes	maximal, characteristic
2	C₄₇×C₈₉	C₉	1	1	yes	characteristic, direct product factor, Hall
3	C₉×C₈₉	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₉×C₄₇	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₈₉	C₃×C₄₇	1	1	yes	characteristic
6	C₃×C₄₇	C₃×C₈₉	1	1	yes	characteristic
7	C₈₉	C₉×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
8	C₄₇	C₉×C₈₉	1	1	yes	characteristic, direct product factor, Sylow
9	C₉	C₄₇×C₈₉	1	1	yes	characteristic, direct product factor, Sylow
10	C₃	C₃×C₄₇×C₈₉	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.