Subgroups — C₉×C₂₃×D₄₇ #34085599

Order 19458.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₂₃×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₂₃×D₄₇	C₃	1	1	yes	maximal, characteristic
3	C₃×C₂₃×C₄₇	C₂×C₃	1	1	yes	characteristic
4	C₂₃×D₄₇	C₉	1	1	yes	characteristic, direct product factor, Hall
5	C₂₃×C₄₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
6	C₉×D₄₇	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₉×C₄₇	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
8	C₂×C₉×C₂₃	—	47	1	no	maximal, Hall
9	C₃×D₄₇	C₃×C₂₃	1	1	yes	characteristic
10	C₉×C₂₃	D₄₇	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₄₇	C₂×C₃×C₂₃	1	1	yes	characteristic
12	C₂×C₃×C₂₃	—	47	1	no	—
13	D₄₇	C₉×C₂₃	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₂₃	C₃×D₄₇	1	1	yes	characteristic
15	C₄₇	C₂×C₉×C₂₃	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₂₃	—	47	1	no	Hall
17	C₂₃	C₉×D₄₇	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₉	—	47	1	no	Hall
19	C₉	C₂₃×D₄₇	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	—	47	1	no	—
21	C₃	C₃×C₂₃×D₄₇	1	1	yes	characteristic
22	C₂	—	47	1	no	Sylow

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.