Subgroups — #14546318

Order 2187.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624550	C₃	1	1	yes	maximal, characteristic
2	#10624445	C₃	1	3	yes	maximal
3	C₃×C₉⋊C₉	—	3	2	no	—
4	C₃×C₉²	C₃²	1	1	yes	characteristic
5	C₃²⋊C₂₇	—	3	3	no	—
6	#6855	—	3	1	no	—
7	#6855	C₉	1	3	yes	—
8	C₃²×C₉	—	3	3	no	—
9	C₃²×C₉	C₃×C₉	1	1	yes	characteristic
10	C₃²×C₉	H(3,𝔽₃)	1	1	yes	characteristic
11	C₃²×C₉	3₋¹⁺²	1	2	yes	—
12	C₃×C₂₇	—	9	3	no	—
13	C₉⋊C₉	—	9	6	no	—
14	C₉²	—	3	3	no	—
15	C₃³	C₃²⋊C₉	1	1	yes	characteristic
16	C₃×C₉	—	3	2	no	—
17	C₃×C₉	—	3	6	no	—
18	C₃×C₉	—	3	1	no	—
19	C₃×C₉	—	3	3	no	—
20	C₃×C₉	—	9	1	no	—
21	C₃×C₉	—	9	6	no	—
22	C₃×C₉	—	9	3	no	—
23	C₃×C₉	—	9	3	no	—
24	C₃×C₉	#731	1	3	yes	—
25	C₂₇	—	27	3	no	—
26	C₃²	—	3	1	no	—
27	C₃²	—	3	2	no	—
28	C₃²	#6867	1	1	yes	characteristic
29	C₃²	#6872	1	3	yes	—
30	C₉	—	3	3	no	—
31	C₉	—	3	6	no	—
32	C₉	—	9	1	no	—
33	C₉	—	27	3	no	—
34	C₃	—	3	3	no	—
35	C₃	#10624457	1	1	yes	characteristic
36	C₃	#10624512	1	1	yes	characteristic
37	C₃	#10624516	1	2	yes	—

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

subgroup	index
#10624550	3
#10624445	3