Subgroups — #11757435

Order 972.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#732	C₃	1	1	yes	maximal, characteristic, complemented
2	#66359	C₃	1	1	yes	maximal, characteristic, complemented
3	#66358	C₃	1	1	yes	maximal, characteristic, complemented
4	C₉⋊(C₂²⋊C₉)	C₃	1	1	yes	maximal, characteristic, complemented
5	#6881	—	4	1	no	maximal, Sylow
6	C₂×#732	—	3	1	no	—
7	C₂²×H(3,𝔽₃)	—	3	1	no	—
8	C₂²×C₃×C₉	C₃²	1	1	yes	characteristic
9	C₂²⋊H(3,𝔽₃)	—	3	1	no	—
10	#1094	—	3	1	no	—
11	C₃×C₂²⋊C₉	—	3	1	no	—
12	#733	—	4	1	no	—
13	#732	—	4	1	no	—
14	#732	A₄	1	1	yes	characteristic, complemented
15	C₉⋊C₉	—	4	1	no	—
16	C₂×H(3,𝔽₃)	—	3	3	no	—
17	C₂×C₃×C₉	—	3	1	no	—
18	C₂²×C₃²	—	9	1	no	—
19	C₂²×C₃²	H(3,𝔽₃)	1	1	yes	characteristic
20	C₃×A₄	—	9	1	no	—
21	C₂²×C₉	—	3	1	no	—
22	C₂²⋊C₉	—	9	1	no	—
23	C₂²⋊C₉	—	9	1	no	—
24	3₋¹⁺²	—	12	1	no	—
25	H(3,𝔽₃)	—	3	1	no	—
26	H(3,𝔽₃)	—	12	1	no	—
27	C₃×C₉	—	12	1	no	—
28	C₃×C₉	C₃×A₄	1	1	yes	characteristic
29	C₂×C₃²	—	3	1	no	—
30	C₂×C₃²	—	9	3	no	—
31	C₂×C₉	—	9	1	no	—
32	C₂²×C₃	—	3	1	no	—
33	C₂²×C₃	—	27	1	no	—
34	C₂²×C₃	#732	1	1	yes	characteristic
35	A₄	—	27	1	no	—
36	C₃²	—	9	1	no	—
37	C₃²	—	36	1	no	—
38	C₃²	C₂²⋊H(3,𝔽₃)	1	1	yes	characteristic
39	C₉	—	3	1	no	—
40	C₉	—	36	1	no	—
41	C₉	—	36	1	no	—
42	C₂×C₃	—	3	1	no	—
43	C₂×C₃	—	9	1	no	—
44	C₂×C₃	—	27	3	no	—
45	C₂²	#6881	1	1	yes	characteristic, complemented, Sylow
46	C₃	—	3	1	no	—
47	C₃	—	27	1	no	—
48	C₃	—	108	1	no	—
49	C₃	#66362	1	1	yes	characteristic
50	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.