Subgroups — #37523974

Order 22923.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21439427	C₃	1	2	yes	maximal, complemented
2	#21439426	C₃	1	3	yes	maximal, complemented
3	#21439425	C₃	1	3	yes	maximal, complemented
4	C₃²⋊(C₂₈₃⋊C₃)	C₃	1	1	yes	maximal, characteristic
5	C₉×C₂₈₃⋊C₃	C₃	1	3	yes	maximal, complemented
6	C₃×C₉×C₂₈₃	C₃	1	1	yes	maximal, characteristic, complemented
7	C₃²×C₂₈₃	C₃²	1	1	yes	characteristic
8	C₃×C₂₈₃⋊C₃	C₃²	1	3	yes	—
9	C₉×C₂₈₃	C₃²	1	1	yes	characteristic
10	C₉×C₂₈₃	C₃²	1	1	yes	characteristic
11	C₉×C₂₈₃	C₃²	1	1	yes	characteristic
12	C₂₈₃⋊C₉	C₃²	1	6	yes	—
13	C₃×C₂₈₃	—	3	1	no	—
14	C₃×C₂₈₃	C₃³	1	1	yes	characteristic
15	C₂₈₃⋊C₃	—	3	3	no	—
16	C₂₈₃	#737	1	1	yes	characteristic, complemented, Sylow
17	#737	—	283	1	no	maximal, Sylow
18	3₋¹⁺²	—	283	2	no	—
19	3₋¹⁺²	—	283	3	no	—
20	3₋¹⁺²	—	283	3	no	—
21	H(3,𝔽₃)	—	283	1	no	—
22	C₃×C₉	—	283	3	no	—
23	C₃×C₉	C₂₈₃⋊C₃	1	1	yes	characteristic, complemented
24	C₃²	—	283	3	no	—
25	C₃²	C₃×C₂₈₃⋊C₃	1	1	yes	characteristic
26	C₉	—	283	6	no	—
27	C₉	C₃×C₂₈₃⋊C₃	1	1	yes	characteristic
28	C₉	C₃×C₂₈₃⋊C₃	1	1	yes	characteristic
29	C₉	C₃×C₂₈₃⋊C₃	1	1	yes	characteristic
30	C₃	—	3	1	no	—
31	C₃	—	849	3	no	—
32	C₃	C₃²×C₂₈₃⋊C₃	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.