Subgroups — #14546151

Order 2187.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624710	C₃	1	3	yes	maximal
2	C₃×C₉×C₂₇	C₃	1	1	yes	maximal, characteristic
3	C₃²×C₂₇	C₉	1	3	yes	—
4	C₃×C₉²	C₃²	1	1	yes	characteristic
5	C₉⋊C₂₇	—	3	6	no	—
6	C₃²⋊C₂₇	C₉	1	9	yes	—
7	C₉×C₂₇	—	3	1	no	—
8	C₉×C₂₇	—	3	3	no	—
9	C₉×C₂₇	—	3	2	no	—
10	C₃²×C₉	C₃×C₉	1	3	yes	—
11	C₃²×C₉	C₃×C₉	1	1	yes	characteristic
12	C₃×C₂₇	—	3	3	no	—
13	C₃×C₂₇	—	3	6	no	—
14	C₃×C₂₇	—	3	9	no	—
15	C₃×C₂₇	C₂₇	1	9	yes	complemented
16	C₉²	H(3,𝔽₃)	1	1	yes	characteristic
17	C₉²	3₋¹⁺²	1	2	yes	—
18	C₉²	3₋¹⁺²	1	6	yes	—
19	C₃³	C₉²	1	1	yes	characteristic
20	C₃×C₉	—	3	9	no	—
21	C₃×C₉	C₃²⋊C₉	1	1	yes	characteristic
22	C₃×C₉	C₃²⋊C₉	1	3	yes	—
23	C₃×C₉	C₉⋊C₉	1	6	yes	—
24	C₃×C₉	C₉⋊C₉	1	2	yes	—
25	C₃×C₉	C₃×C₂₇	1	3	yes	—
26	C₃×C₉	C₂₇⋊C₃	1	6	yes	—
27	C₂₇	—	3	9	no	—
28	C₂₇	—	9	9	no	—
29	C₃²	—	3	3	no	—
30	C₃²	#6855	1	1	yes	characteristic
31	C₃²	C₉×C₂₇	1	1	yes	characteristic
32	C₃²	#6864	1	2	yes	—
33	C₉	—	3	6	no	—
34	C₉	C₃²⋊C₂₇	1	3	yes	—
35	C₉	#6873	1	9	yes	—
36	C₉	C₉⋊C₂₇	1	6	yes	—
37	C₃	—	3	1	no	—
38	C₃	—	3	2	no	—
39	C₃	#10624463	1	1	yes	characteristic
40	C₃	#10624468	1	3	yes	—

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

N	H ≅ G/N	type
15. C₃×C₂₇	C₂₇	semidirect

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

subgroup	index
#10624710	3
C₃×C₉×C₂₇	3