Subgroups — #14550358

Order 2187.

221 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624706	C₃	1	2	yes	maximal
2	C₉×C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
3	#10624554	C₃	1	1	yes	maximal, characteristic
4	#10624472	C₃	1	9	yes	maximal
5	C₃×C₂₇⋊C₃	C₃²	1	6	yes	—
6	C₃×C₂₇⋊C₃	C₃²	1	3	yes	—
7	C₃×C₉⋊C₉	—	3	3	no	—
8	C₃×C₉⋊C₉	C₃²	1	3	yes	—
9	C₃×C₉²	C₃²	1	1	yes	characteristic
10	C₉⋊C₂₇	—	3	6	no	—
11	#6864	C₉	1	6	yes	complemented
12	C₉×C₂₇	C₉	1	3	yes	complemented
13	C₃²×C₉	—	3	3	no	—
14	C₃²×C₉	3₋¹⁺²	1	3	yes	—
15	C₃²×C₉	C₃³	1	1	yes	characteristic
16	C₂₇⋊C₃	—	3	9	no	—
17	C₂₇⋊C₃	—	3	18	no	—
18	C₃×C₂₇	—	3	6	no	—
19	C₃×C₂₇	C₃×C₉	1	9	yes	—
20	C₉⋊C₉	—	3	9	no	—
21	C₉⋊C₉	—	9	9	no	—
22	C₉²	C₃×C₉	1	1	yes	characteristic
23	C₉²	C₃×C₉	1	2	yes	—
24	C₉²	3₋¹⁺²	1	6	yes	—
25	C₃³	C₃×3₋¹⁺²	1	1	yes	characteristic
26	C₃×C₉	—	3	9	no	—
27	C₃×C₉	—	9	9	no	—
28	C₃×C₉	—	9	3	no	—
29	C₃×C₉	C₉⋊C₉	1	6	yes	—
30	C₃×C₉	C₉⋊C₉	1	3	yes	—
31	C₃×C₉	C₃²×C₉	1	1	yes	characteristic
32	C₃×C₉	C₃×3₋¹⁺²	1	2	yes	—
33	C₃×C₉	#737	1	9	yes	—
34	C₂₇	—	3	9	no	—
35	C₂₇	—	9	6	no	—
36	C₃²	—	3	3	no	—
37	C₃²	C₃×C₉⋊C₉	1	1	yes	characteristic
38	C₃²	#6899	1	3	yes	—
39	C₉	—	3	6	no	—
40	C₉	—	27	3	no	—
41	C₉	#6875	1	9	yes	—
42	C₉	#6887	1	3	yes	—
43	C₉	#6899	1	6	yes	—
44	C₃	—	3	3	no	—
45	C₃	#10624553	1	1	yes	characteristic
46	C₃	C₃×#6875	1	3	yes	—

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

N	H ≅ G/N	type
11. #6864	C₉	semidirect
12. C₉×C₂₇	C₉	semidirect

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