Subgroups — #14551991

Order 2187.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#6880	C₃	1	3	yes	maximal
2	C₉×C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
3	#10624536	C₃	1	9	yes	maximal, complemented
4	C₃×#733	—	3	3	no	—
5	C₃×C₂₇⋊C₃	—	3	1	no	—
6	C₃×C₉²	C₃²	1	1	yes	characteristic
7	#6880	—	3	6	no	—
8	#6880	C₃²	1	9	yes	—
9	#6864	—	3	2	no	—
10	C₉×C₂₇	C₃²	1	3	yes	—
11	C₃×3₋¹⁺²	—	9	3	no	—
12	C₃²×C₉	—	3	1	no	—
13	C₃²×C₉	H(3,𝔽₃)	1	1	yes	characteristic
14	#733	—	3	9	no	—
15	#733	—	9	6	no	—
16	C₂₇⋊C₃	—	3	9	no	—
17	C₃×C₂₇	—	3	3	no	—
18	C₉²	—	3	2	no	—
19	C₉²	H(3,𝔽₃)	1	2	yes	—
20	C₉²	C₃³	1	1	yes	characteristic
21	C₃³	#732	1	1	yes	characteristic
22	3₋¹⁺²	—	9	9	no	—
23	3₋¹⁺²	—	27	6	no	—
24	C₃×C₉	—	3	3	no	—
25	C₃×C₉	—	3	1	no	—
26	C₃×C₉	—	3	2	no	—
27	C₃×C₉	—	9	3	no	—
28	C₃×C₉	—	27	3	no	—
29	C₃×C₉	#732	1	2	yes	—
30	C₃×C₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
31	C₂₇	—	3	9	no	—
32	C₃²	—	9	1	no	—
33	C₃²	#6879	1	3	yes	—
34	C₃²	C₃×#732	1	1	yes	characteristic
35	C₉	—	3	3	no	—
36	C₉	—	3	1	no	—
37	C₉	—	3	2	no	—
38	C₉	—	9	2	no	—
39	C₉	—	27	9	no	—
40	C₃	—	3	1	no	—
41	C₃	—	3	3	no	—
42	C₃	C₃×#6879	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃	C₃×#6879
commutator, Frattini, cosocle	C₉²	C₃³
prime radical	C₃³	#732
LCS	G ▷ C₉² ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃ ◁ C₃³ ◁ C₃²×C₉ ◁ C₃×C₉² ◁ G
LECS	G ▷ C₉² ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁

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

N	H ≅ G/N	type
3. #10624536	C₃	semidirect

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