Subgroups — #92183

Order 486.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6873	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	#4208	C₃	1	1	yes	maximal, characteristic
3	D₃×C₂₇	—	3	1	no	maximal
4	#737	C₂×C₃	1	1	yes	characteristic
5	C₂₇⋊C₃	—	2	1	no	—
6	C₃×C₂₇	D₃	1	1	yes	characteristic, complemented
7	#272	C₉	1	1	yes	characteristic
8	D₃×C₉	—	3	1	no	—
9	D₃×C₉	—	9	1	no	—
10	C₂×C₂₇	—	9	1	no	—
11	3₋¹⁺²	—	2	1	no	—
12	3₋¹⁺²	—	6	1	no	—
13	H(3,𝔽₃)	C₂×C₉	1	1	yes	characteristic
14	C₃×C₉	—	3	1	no	—
15	C₃×C₉	C₃×D₃	1	1	yes	characteristic
16	C₂₇	—	3	1	no	—
17	C₂₇	—	6	1	no	—
18	C₃×D₃	—	3	1	no	—
19	C₃×D₃	—	9	1	no	—
20	C₂×C₉	—	9	1	no	—
21	C₃²	—	3	1	no	—
22	C₃²	D₃×C₉	1	1	yes	characteristic
23	C₉	—	2	1	no	—
24	C₉	—	6	1	no	—
25	C₉	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
26	C₂×C₃	—	9	1	no	—
27	D₃	—	3	1	no	—
28	D₃	—	9	1	no	—
29	C₃	—	3	1	no	—
30	C₃	—	9	1	no	—
31	C₃	(C₃⋊D₃)⋊C₉	1	1	yes	characteristic
32	C₂	—	9	1	no	Sylow

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

N	H ≅ G/N	type
1. #6873	C₂	semidirect
6. C₃×C₂₇	D₃	semidirect

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