Subgroups — #11757761

Order 972.

163 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉⋊A₄	C₃	1	4	yes	maximal
2	C₂²×C₉²	C₃	1	1	yes	maximal, characteristic, complemented
3	C₉⋊(C₂²⋊C₉)	C₃	1	8	yes	maximal, complemented
4	#6900	—	4	1	no	maximal, Sylow
5	C₂×C₉²	—	3	1	no	—
6	C₃²×A₄	C₃²	1	1	yes	characteristic
7	C₂²×C₃×C₉	C₃²	1	4	yes	—
8	C₃×C₂²⋊C₉	C₃²	1	8	yes	—
9	C₉⋊A₄	—	3	12	no	—
10	C₃×3₋¹⁺²	—	4	4	no	—
11	C₉⋊C₉	—	4	8	no	—
12	C₉²	A₄	1	1	yes	characteristic, complemented
13	C₂×C₃×C₉	—	3	4	no	—
14	C₂²×C₃²	C₃³	1	1	yes	characteristic
15	C₃×A₄	—	3	4	no	—
16	C₂²×C₉	3₋¹⁺²	1	12	yes	complemented
17	C₂²⋊C₉	—	3	8	no	—
18	C₃³	—	4	1	no	—
19	3₋¹⁺²	—	12	12	no	—
20	C₃×C₉	—	4	8	no	—
21	C₃×C₉	C₃×A₄	1	4	yes	—
22	C₂×C₃²	—	3	1	no	—
23	C₂×C₉	—	3	12	no	—
24	C₂²×C₃	C₃×3₋¹⁺²	1	4	yes	—
25	A₄	—	9	1	no	—
26	C₃²	—	12	4	no	—
27	C₃²	C₃²×A₄	1	1	yes	characteristic
28	C₉	—	12	8	no	—
29	C₉	C₉⋊A₄	1	12	yes	complemented
30	C₂×C₃	—	3	4	no	—
31	C₂²	#6900	1	1	yes	characteristic, complemented, Sylow
32	C₃	—	36	1	no	—
33	C₃	C₃×C₉⋊A₄	1	4	yes	—
34	C₂	—	3	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.