Subgroups — #14546320

Order 2187.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624551	C₃	1	1	yes	maximal, characteristic
2	#10624445	C₃	1	3	yes	maximal
3	C₃×C₉²	C₃²	1	1	yes	characteristic
4	C₃²⋊C₂₇	—	3	3	no	—
5	#6855	—	3	1	no	—
6	#6855	—	3	1	no	—
7	#6855	—	3	1	no	—
8	#6855	C₉	1	3	yes	—
9	C₃²×C₉	—	3	3	no	—
10	C₃²×C₉	C₃×C₉	1	1	yes	characteristic
11	C₃²×C₉	H(3,𝔽₃)	1	1	yes	characteristic
12	C₃²×C₉	3₋¹⁺²	1	1	yes	characteristic
13	C₃²×C₉	3₋¹⁺²	1	1	yes	characteristic
14	C₃×C₂₇	—	9	3	no	—
15	C₉²	—	3	3	no	—
16	C₃³	C₃²⋊C₉	1	1	yes	characteristic
17	C₃×C₉	—	3	1	no	—
18	C₃×C₉	—	3	1	no	—
19	C₃×C₉	—	3	1	no	—
20	C₃×C₉	—	3	3	no	—
21	C₃×C₉	—	9	1	no	—
22	C₃×C₉	—	9	1	no	—
23	C₃×C₉	—	9	1	no	—
24	C₃×C₉	—	9	3	no	—
25	C₃×C₉	—	9	3	no	—
26	C₃×C₉	—	9	3	no	—
27	C₃×C₉	—	9	3	no	—
28	C₃×C₉	#731	1	3	yes	—
29	C₂₇	—	27	3	no	—
30	C₃²	—	3	1	no	—
31	C₃²	—	3	1	no	—
32	C₃²	—	3	1	no	—
33	C₃²	#6867	1	1	yes	characteristic
34	C₃²	#6872	1	3	yes	—
35	C₉	—	3	3	no	—
36	C₉	—	9	1	no	—
37	C₉	—	9	1	no	—
38	C₉	—	9	1	no	—
39	C₉	—	27	3	no	—
40	C₃	—	3	3	no	—
41	C₃	#10624457	1	1	yes	characteristic
42	C₃	#10624514	1	1	yes	characteristic
43	C₃	#10624515	1	1	yes	characteristic
44	C₃	#10624517	1	1	yes	characteristic

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

subgroup	index
#10624551	3
#10624445	3