Subgroups — C₃×#10624943 #14555448

Order 2187.

57356 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624943	C₃	1	243	yes	maximal, direct product factor
2	C₃×3₋¹⁺⁴	C₃	1	80	yes	maximal, complemented
3	C₃×H(5,𝔽₃)	C₃	1	1	yes	maximal, characteristic
4	C₃²×#737	C₃	1	40	yes	maximal, complemented
5	3₋¹⁺⁴	C₃²	1	6480	yes	complemented
6	H(5,𝔽₃)	C₃²	1	81	yes	—
7	C₃×#737	C₃²	1	90	yes	complemented
8	C₃×#737	C₃²	1	720	yes	complemented
9	C₃×#737	C₃²	1	3240	yes	complemented
10	C₃²×3₋¹⁺²	C₃²	1	320	yes	complemented
11	C₃²×H(3,𝔽₃)	C₃²	1	40	yes	—
12	C₃³×C₉	C₃²	1	40	yes	complemented
13	C₃⁴	C₃³	1	40	yes	—
14	#737	C₃³	1	2430	yes	complemented
15	#737	C₃³	1	19440	yes	complemented
16	C₃×3₋¹⁺²	C₃³	1	720	yes	—
17	C₃×3₋¹⁺²	C₃³	1	8640	yes	complemented
18	C₃×H(3,𝔽₃)	C₃³	1	90	yes	—
19	C₃×H(3,𝔽₃)	C₃³	1	1080	yes	—
20	C₃²×C₉	C₃³	1	320	yes	—
21	C₃²×C₉	C₃³	1	40	yes	—
22	C₃²×C₉	C₃³	1	1080	yes	complemented
23	C₃³	—	9	120	no	—
24	C₃³	C₃⁴	1	40	yes	—
25	C₃³	C₃⁴	1	360	yes	—
26	3₋¹⁺²	C₃⁴	1	6480	yes	—
27	H(3,𝔽₃)	C₃⁴	1	810	yes	—
28	C₃×C₉	C₃⁴	1	80	yes	—
29	C₃×C₉	C₃⁴	1	360	yes	—
30	C₃×C₉	C₃⁴	1	2880	yes	—
31	C₃×C₉	C₃⁴	1	1	yes	characteristic
32	C₃²	—	3	120	no	—
33	C₃²	—	9	360	no	—
34	C₃²	C₃⁵	1	120	yes	—
35	C₃²	C₃⁵	1	1	yes	characteristic
36	C₉	C₃⁵	1	3	yes	—
37	C₉	C₃⁵	1	240	yes	—
38	C₃	—	3	120	no	—
39	C₃	#10624943	1	3	yes	direct product factor
40	C₃	C₃⁶	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₉	C₃⁴
commutator, Frattini, cosocle	C₃	C₃⁶
socle	C₃²	C₃⁵
prime radical	C₃×H(5,𝔽₃)	C₃
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₉ ◁ G
LECS	G ▷ C₃ ▷ C₁

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.