Subgroups — C₃×#10624562 #14552151

Order 2187.

14228 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×H(3,𝔽₃)	C₃	1	13	yes	maximal, complemented
2	#10624562	C₃	1	27	yes	maximal, direct product factor
3	C₃⁵	C₃²	1	13	yes	—
4	C₃²×H(3,𝔽₃)	—	3	468	no	—
5	C₃²×H(3,𝔽₃)	C₃²	1	117	yes	complemented
6	C₃⁴	—	3	468	no	—
7	C₃⁴	H(3,𝔽₃)	1	117	yes	complemented
8	C₃⁴	C₃³	1	39	yes	—
9	C₃⁴	C₃³	1	1	yes	characteristic
10	C₃×H(3,𝔽₃)	—	3	3159	no	—
11	C₃×H(3,𝔽₃)	—	3	1404	no	—
12	C₃³	—	3	468	no	—
13	C₃³	—	3	1404	no	—
14	C₃³	—	9	1053	no	—
15	C₃³	C₃×H(3,𝔽₃)	1	39	yes	—
16	C₃³	C₃×H(3,𝔽₃)	1	117	yes	complemented
17	C₃³	C₃⁴	1	1	yes	characteristic
18	H(3,𝔽₃)	—	3	3159	no	—
19	C₃²	—	3	468	no	—
20	C₃²	—	9	1053	no	—
21	C₃²	—	9	351	no	—
22	C₃²	C₃²⋊H(3,𝔽₃)	1	117	yes	—
23	C₃²	C₃²×H(3,𝔽₃)	1	13	yes	—
24	C₃	—	9	117	no	—
25	C₃	#10624562	1	27	yes	direct product factor
26	C₃	C₃×C₃²⋊H(3,𝔽₃)	1	13	yes	—

	subgroup	G/H
center, socle	C₃⁴	C₃³
commutator, Frattini, cosocle	C₃³	C₃⁴
LCS	G ▷ C₃³ ▷ C₁
UCS	C₁ ◁ C₃⁴ ◁ G
LECS	G ▷ C₃³ ▷ 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.

subgroup	index
C₃³×H(3,𝔽₃)	3
#10624562	3