Subgroups — #14546237

Order 2187.

107 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624544	C₃	1	1	yes	maximal, characteristic
2	#10624445	C₃	1	3	yes	maximal
3	C₃×C₉²	C₉	1	2	yes	—
4	C₃×C₉²	C₉	1	1	yes	characteristic
5	C₃×C₉²	C₃²	1	1	yes	characteristic
6	C₃²⋊C₂₇	—	3	3	no	—
7	#6855	—	3	1	no	—
8	#6855	—	3	2	no	—
9	C₃²×C₉	—	3	1	no	—
10	C₃²×C₉	—	3	2	no	—
11	C₃²×C₉	C₃×C₉	1	1	yes	characteristic
12	C₃²×C₉	H(3,𝔽₃)	1	1	yes	characteristic
13	C₃²×C₉	3₋¹⁺²	1	2	yes	—
14	C₃×C₂₇	—	9	3	no	—
15	C₉²	—	3	6	no	—
16	C₉²	—	3	2	no	—
17	C₉²	—	3	3	no	—
18	C₉²	C₂₇	1	3	yes	complemented
19	C₃³	C₃²⋊C₉	1	1	yes	characteristic
20	C₃×C₉	—	3	1	no	—
21	C₃×C₉	—	3	2	no	—
22	C₃×C₉	—	3	3	no	—
23	C₃×C₉	—	3	2	no	—
24	C₃×C₉	—	3	6	no	—
25	C₃×C₉	—	9	1	no	—
26	C₃×C₉	—	9	1	no	—
27	C₃×C₉	—	9	2	no	—
28	C₃×C₉	—	9	2	no	—
29	C₃×C₉	—	9	4	no	—
30	C₃×C₉	—	9	2	no	—
31	C₃×C₉	C₃×C₂₇	1	1	yes	characteristic
32	C₃×C₉	C₂₇⋊C₃	1	2	yes	—
33	C₃×C₉	#731	1	3	yes	—
34	C₂₇	—	27	3	no	—
35	C₃²	—	3	1	no	—
36	C₃²	—	3	2	no	—
37	C₃²	C₃²⋊C₂₇	1	1	yes	characteristic
38	C₃²	#6867	1	1	yes	characteristic
39	C₃²	#6869	1	2	yes	—
40	C₉	—	3	3	no	—
41	C₉	—	3	1	no	—
42	C₉	—	3	2	no	—
43	C₉	—	9	3	no	—
44	C₉	—	9	6	no	—
45	C₉	—	9	2	no	—
46	C₃	—	3	1	no	—
47	C₃	—	3	2	no	—
48	C₃	#10624445	1	1	yes	characteristic
49	C₃	#10624512	1	1	yes	characteristic
50	C₃	#10624514	1	2	yes	—

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

N	H ≅ G/N	type
18. C₉²	C₂₇	semidirect

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

subgroup	index
#10624544	3
#10624445	3