Subgroups — #14550348

Order 2187.

199 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624709	C₃	1	6	yes	maximal
2	#10624681	C₃	1	1	yes	maximal, characteristic
3	#10624468	C₃	1	3	yes	maximal
4	#10624465	C₃	1	2	yes	maximal
5	H(3,ℤ/9)	C₃	1	1	yes	maximal, characteristic
6	C₃×C₂₇⋊C₃	C₃²	1	6	yes	—
7	C₃×C₂₇⋊C₃	C₃²	1	2	yes	—
8	C₃²×C₂₇	C₃²	1	1	yes	characteristic
9	#6887	C₃²	1	3	yes	—
10	#6887	C₃²	1	1	yes	characteristic
11	#6875	—	3	18	no	—
12	#6864	C₉	1	6	yes	complemented
13	C₉×C₂₇	C₉	1	3	yes	complemented
14	C₃²×C₉	C₃³	1	1	yes	characteristic
15	C₂₇⋊C₃	—	3	12	no	—
16	C₂₇⋊C₃	—	3	6	no	—
17	C₂₇⋊C₃	3₋¹⁺²	1	18	yes	—
18	C₃×C₂₇	—	3	3	no	—
19	C₃×C₂₇	—	3	6	no	—
20	C₃×C₂₇	C₃×C₉	1	1	yes	characteristic
21	C₃×C₂₇	C₃×C₉	1	2	yes	—
22	C₃×C₂₇	C₃×C₉	1	6	yes	—
23	C₉⋊C₉	—	3	2	no	—
24	C₉⋊C₉	—	3	6	no	—
25	C₃²⋊C₉	—	3	1	no	—
26	C₃²⋊C₉	—	3	3	no	—
27	C₉²	—	3	3	no	—
28	C₉²	C₃×C₉	1	3	yes	—
29	C₃³	#737	1	1	yes	characteristic
30	C₃×C₉	—	3	3	no	—
31	C₃×C₉	—	9	3	no	—
32	C₃×C₉	C₃²×C₉	1	1	yes	characteristic
33	C₃×C₉	C₃×3₋¹⁺²	1	6	yes	—
34	C₃×C₉	#737	1	3	yes	—
35	C₃×C₉	#737	1	2	yes	—
36	C₂₇	—	3	1	no	—
37	C₂₇	—	3	2	no	—
38	C₂₇	—	9	6	no	—
39	C₂₇	C₉⋊C₉	1	18	yes	—
40	C₃²	—	9	1	no	—
41	C₃²	#6887	1	1	yes	characteristic
42	C₃²	#6896	1	3	yes	—
43	C₉	—	9	3	no	—
44	C₉	—	27	3	no	—
45	C₉	C₃×C₉⋊C₉	1	2	yes	—
46	C₉	#6887	1	1	yes	characteristic
47	C₉	#6896	1	6	yes	—
48	C₃	—	3	1	no	—
49	C₃	—	3	3	no	—
50	C₃	#10624550	1	1	yes	characteristic

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

N	H ≅ G/N	type
12. #6864	C₉	semidirect
13. C₉×C₂₇	C₉	semidirect

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