Subgroups — #11757420

Order 972.

55 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
2	#66359	C₃	1	3	yes	maximal
3	#6882	—	4	1	no	maximal, Sylow
4	C₂×C₉⋊C₉	—	3	1	no	—
5	C₂²×C₃×C₉	—	3	1	no	—
6	C₂²×C₃×C₉	C₃²	1	1	yes	characteristic
7	#1094	—	3	3	no	—
8	#733	—	4	3	no	—
9	C₉⋊C₉	A₄	1	1	yes	characteristic
10	C₂×C₃×C₉	—	3	1	no	—
11	C₂×C₃×C₉	—	3	3	no	—
12	C₂²×C₃²	H(3,𝔽₃)	1	1	yes	characteristic
13	C₂²×C₉	—	3	1	no	—
14	C₂²×C₉	—	9	1	no	—
15	C₂²⋊C₉	—	9	3	no	—
16	3₋¹⁺²	—	12	3	no	—
17	C₃×C₉	—	3	1	no	—
18	C₃×C₉	C₃×A₄	1	1	yes	characteristic
19	C₂×C₃²	—	3	1	no	—
20	C₂×C₉	—	3	3	no	—
21	C₂×C₉	—	9	3	no	—
22	C₂²×C₃	—	3	1	no	—
23	C₂²×C₃	#732	1	1	yes	characteristic
24	C₃²	C₂²⋊H(3,𝔽₃)	1	1	yes	characteristic
25	C₉	—	3	1	no	—
26	C₉	—	9	1	no	—
27	C₉	—	36	3	no	—
28	C₂×C₃	—	3	3	no	—
29	C₂×C₃	—	3	1	no	—
30	C₂²	#6882	1	1	yes	characteristic, complemented, Sylow
31	C₃	—	3	1	no	—
32	C₃	#66358	1	1	yes	characteristic
33	C₂	—	3	1	no	—

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

N	H ≅ G/N	type
30. C₂²	#6882	semidirect

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