Subgroups — #14550332

Order 2187.

308 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#6887	C₃	1	1	yes	maximal, characteristic
2	#10624683	C₃	1	3	yes	maximal
3	#10624467	C₃	1	9	yes	maximal, complemented
4	C₃³×C₉	C₃²	1	1	yes	characteristic
5	C₃×C₂₇⋊C₃	C₃²	1	9	yes	—
6	#6887	—	3	3	no	—
7	#6887	—	3	6	no	—
8	C₃×C₉⋊C₉	C₉	1	6	yes	—
9	C₃×C₃²⋊C₉	C₉	1	3	yes	—
10	C₃×C₉²	C₃²	1	3	yes	—
11	C₃²⋊C₂₇	—	3	9	no	—
12	C₃⁴	C₃×C₉	1	1	yes	characteristic
13	C₃²×C₉	—	3	9	no	—
14	C₃²×C₉	C₃×C₉	1	2	yes	—
15	C₃²×C₉	C₃×C₉	1	9	yes	—
16	C₃²×C₉	H(3,𝔽₃)	1	3	yes	—
17	C₃²×C₉	3₋¹⁺²	1	6	yes	—
18	C₃²×C₉	C₃³	1	1	yes	characteristic
19	C₂₇⋊C₃	—	3	27	no	—
20	C₃×C₂₇	—	3	9	no	—
21	C₉⋊C₉	—	3	18	no	—
22	C₃²⋊C₉	—	3	9	no	—
23	C₉²	—	3	3	no	—
24	C₉²	—	3	6	no	—
25	C₃³	—	3	3	no	—
26	C₃³	—	9	3	no	—
27	C₃³	C₃²⋊C₉	1	3	yes	—
28	C₃³	C₃²×C₉	1	1	yes	characteristic
29	C₃×C₉	—	3	6	no	—
30	C₃×C₉	—	3	9	no	—
31	C₃×C₉	—	3	18	no	—
32	C₃×C₉	—	3	9	no	—
33	C₃×C₉	—	9	9	no	—
34	C₃×C₉	C₃²⋊C₉	1	6	yes	—
35	C₃×C₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
36	C₃×C₉	C₃×3₋¹⁺²	1	2	yes	—
37	C₃×C₉	#737	1	9	yes	—
38	C₂₇	—	9	9	no	—
39	C₃²	—	3	3	no	—
40	C₃²	—	3	3	no	—
41	C₃²	—	3	9	no	—
42	C₃²	—	9	9	no	—
43	C₃²	C₃×C₃²⋊C₉	1	1	yes	characteristic
44	C₃²	#6887	1	3	yes	—
45	C₉	—	3	6	no	—
46	C₉	—	9	9	no	—
47	C₉	#6893	1	3	yes	—
48	C₉	#6895	1	6	yes	—
49	C₃	—	3	3	no	—
50	C₃	—	9	3	no	—
51	C₃	#10624549	1	1	yes	characteristic
52	C₃	#10624694	1	3	yes	—

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

N	H ≅ G/N	type
3. #10624467	C₃	semidirect

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