Subgroups — #11757764

Order 972.

123 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₉²	C₃	1	1	yes	maximal, characteristic, complemented
2	(C₃×A₄)⋊C₉	C₃	1	4	yes	maximal
3	(C₂²⋊C₉)⋊C₉	C₃	1	8	yes	maximal, complemented
4	#6898	—	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⋊C₉	—	4	8	no	—
10	C₃²⋊C₉	—	4	4	no	—
11	C₉²	A₄	1	1	yes	characteristic, complemented
12	C₂×C₃×C₉	—	3	4	no	—
13	C₂²×C₃²	C₃³	1	1	yes	characteristic
14	C₃×A₄	—	3	4	no	—
15	C₂²×C₉	—	3	4	no	—
16	C₂²⋊C₉	—	3	8	no	—
17	C₃³	—	4	1	no	—
18	C₃×C₉	—	4	8	no	—
19	C₃×C₉	C₃×A₄	1	4	yes	—
20	C₂×C₃²	—	3	1	no	—
21	C₂×C₉	—	3	12	no	—
22	C₂²×C₃	#737	1	4	yes	—
23	A₄	—	9	1	no	—
24	C₃²	—	12	4	no	—
25	C₃²	C₃²×A₄	1	1	yes	characteristic
26	C₉	—	3	4	no	—
27	C₉	—	12	8	no	—
28	C₂×C₃	—	3	4	no	—
29	C₂²	#6898	1	1	yes	characteristic, complemented, Sylow
30	C₃	—	36	1	no	—
31	C₃	#66436	1	4	yes	—
32	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.