Subgroups — #32915344

Order 18549.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²⋊(C₂₂₉⋊C₃)	C₃	1	2	yes	maximal, complemented
2	C₃×C₂₂₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
3	H(3,𝔽₃)×C₂₂₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃²×C₂₂₉	—	3	1	no	—
5	C₃²×C₂₂₉	C₃²	1	1	yes	characteristic
6	C₃×C₂₂₉⋊C₃	—	3	2	no	—
7	C₂₂₉⋊C₉	—	3	1	no	—
8	C₃×C₂₂₉	—	3	1	no	—
9	C₃×C₂₂₉	—	9	1	no	—
10	C₃×C₂₂₉	H(3,𝔽₃)	1	1	yes	characteristic
11	C₂₂₉⋊C₃	—	9	2	no	—
12	C₂₂₉	#732	1	1	yes	characteristic, complemented, Sylow
13	#732	—	229	1	no	maximal, Sylow
14	H(3,𝔽₃)	—	229	2	no	—
15	H(3,𝔽₃)	C₂₂₉⋊C₃	1	1	yes	characteristic, complemented
16	C₃×C₉	—	229	1	no	—
17	C₃²	—	3	1	no	—
18	C₃²	—	687	2	no	—
19	C₃²	C₃×C₂₂₉⋊C₃	1	1	yes	characteristic
20	C₉	—	687	1	no	—
21	C₃	—	3	1	no	—
22	C₃	—	9	1	no	—
23	C₃	—	2061	2	no	—
24	C₃	C₃²⋊(C₂₂₉⋊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.