Subgroups — #14516727

Order 1944.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11757618	C₂	1	1	yes	maximal, characteristic
2	#10619526	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×#6900	C₄	1	1	yes	characteristic
4	C₃⋊(3₋¹⁺²⋊C₄)	—	6	2	no	—
5	C₉⋊Dic₉	C₂×C₃	1	1	yes	characteristic
6	#6900	C₈	1	1	yes	characteristic, complemented, Sylow
7	C₃×#622	—	9	1	no	maximal
8	C₂×C₃×3₋¹⁺²	—	2	2	no	—
9	C₂×C₉⋊C₉	—	4	2	no	—
10	C₂×C₉²	C₃×C₄	1	1	yes	characteristic
11	C₃×C₃⋊Dic₃	—	9	1	no	—
12	C₃⋊Dic₉	—	6	2	no	—
13	3₋¹⁺²⋊C₄	—	18	6	no	—
14	C₃×3₋¹⁺²	—	2	2	no	—
15	C₉⋊C₉	—	4	2	no	—
16	C₉²	C₃×C₈	1	1	yes	characteristic, complemented
17	#622	—	9	1	no	—
18	C₂×C₃³	#157	1	1	yes	characteristic
19	C₂×3₋¹⁺²	—	6	6	no	—
20	C₂×C₃×C₉	—	2	2	no	—
21	C₂×C₃×C₉	—	4	2	no	—
22	C₃⋊Dic₃	—	9	1	no	—
23	C₃×Dic₃	—	54	2	no	—
24	Dic₉	—	18	6	no	—
25	C₃³	#622	1	1	yes	characteristic
26	3₋¹⁺²	—	6	6	no	—
27	C₃×C₉	—	2	2	no	—
28	C₃×C₉	—	4	2	no	—
29	C₃×C₈	—	81	1	no	—
30	C₂×C₃²	—	6	2	no	—
31	C₂×C₃²	C₃×#157	1	1	yes	characteristic
32	C₂×C₉	—	2	6	no	—
33	C₂×C₉	—	12	2	no	—
34	C₃×C₄	—	81	1	no	—
35	Dic₃	—	54	2	no	—
36	C₃²	—	6	2	no	—
37	C₃²	C₃×#622	1	1	yes	characteristic
38	C₉	—	2	6	no	—
39	C₉	—	12	2	no	—
40	C₈	—	81	1	no	Sylow
41	C₂×C₃	—	2	2	no	—
42	C₂×C₃	—	9	1	no	—
43	C₄	—	81	1	no	—
44	C₃	—	2	2	no	—
45	C₃	—	9	1	no	—
46	C₂	#11757684	1	1	yes	characteristic

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.