Subgroups — #6873

Order 243.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#737	C₃	1	1	yes	maximal, characteristic
2	C₂₇⋊C₃	C₃	1	2	yes	maximal, complemented
3	C₃×C₂₇	C₃	1	1	yes	maximal, characteristic, complemented
4	3₋¹⁺²	—	3	2	no	—
5	3₋¹⁺²	C₉	1	2	yes	—
6	H(3,𝔽₃)	C₉	1	1	yes	characteristic
7	C₃×C₉	—	3	1	no	—
8	C₃×C₉	C₃²	1	1	yes	characteristic
9	C₂₇	—	3	1	no	—
10	C₂₇	—	3	2	no	—
11	C₃²	—	3	1	no	—
12	C₃²	C₃×C₉	1	1	yes	characteristic
13	C₉	—	3	2	no	—
14	C₉	H(3,𝔽₃)	1	1	yes	characteristic
15	C₉	3₋¹⁺²	1	2	yes	—
16	C₃	—	3	1	no	—
17	C₃	—	9	1	no	—
18	C₃	C₃²⋊C₉	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. C₂₇⋊C₃	C₃	semidirect
3. C₃×C₂₇	C₃	semidirect

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