Subgroups — #14517907

Order 1944.

47 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11757684	C₂	1	1	yes	maximal, characteristic
2	#10619732	C₃	1	1	yes	maximal, characteristic, complemented
3	#92314	C₄	1	1	yes	characteristic
4	#66343	C₂×C₃	1	1	yes	characteristic
5	#6900	C₈	1	1	yes	characteristic, complemented, Sylow
6	C₃×AGL(1,𝔽₉)	—	9	1	no	maximal
7	C₃⋊AGL(1,ℤ/9)	—	12	1	no	—
8	C₉⋊D₉	C₃×C₄	1	1	yes	characteristic
9	C₃×#157	—	9	1	no	—
10	C₃×3₋¹⁺²	—	4	1	no	—
11	C₉⋊C₉	—	8	1	no	—
12	C₉²	C₃×C₈	1	1	yes	characteristic, complemented
13	AGL(1,𝔽₉)	—	9	1	no	—
14	C₃×C₃⋊D₃	—	9	1	no	—
15	C₃⋊D₉	—	12	1	no	—
16	AGL(1,ℤ/9)	—	36	3	no	—
17	#157	—	9	1	no	—
18	C₃³	AGL(1,𝔽₉)	1	1	yes	characteristic
19	3₋¹⁺²	—	12	3	no	—
20	C₃×C₉	—	4	1	no	—
21	C₃×C₉	—	8	1	no	—
22	C₃×C₈	—	81	1	no	—
23	C₃⋊D₃	—	9	1	no	—
24	C₃×D₃	—	108	1	no	—
25	D₉	—	36	3	no	—
26	C₃×C₄	—	81	1	no	—
27	C₃²	—	12	1	no	—
28	C₃²	C₃×AGL(1,𝔽₉)	1	1	yes	characteristic
29	C₉	—	4	3	no	—
30	C₉	—	24	1	no	—
31	C₈	—	81	1	no	Sylow
32	C₂×C₃	—	81	1	no	—
33	D₃	—	108	1	no	—
34	C₄	—	81	1	no	—
35	C₃	—	4	1	no	—
36	C₃	—	9	1	no	—
37	C₂	—	81	1	no	—

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

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