Subgroups — #11757436

Order 972.

60 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
2	#66359	C₃	1	2	yes	maximal, complemented
3	C₉×C₂²⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
4	#6878	—	4	1	no	maximal, Sylow
5	C₂×#732	—	3	1	no	—
6	C₂²×H(3,𝔽₃)	—	3	1	no	—
7	C₂²×C₃×C₉	C₃²	1	1	yes	characteristic
8	#1094	—	3	2	no	—
9	C₃×C₂²⋊C₉	—	3	1	no	—
10	#733	—	4	2	no	—
11	#732	A₄	1	1	yes	characteristic
12	C₉²	—	4	1	no	—
13	C₂×H(3,𝔽₃)	—	3	3	no	—
14	C₂×C₃×C₉	—	3	1	no	—
15	C₂²×C₃²	—	9	1	no	—
16	C₂²×C₃²	H(3,𝔽₃)	1	1	yes	characteristic
17	C₂²×C₉	—	3	1	no	—
18	C₂²⋊C₉	—	3	3	no	—
19	C₂²⋊C₉	—	9	2	no	—
20	3₋¹⁺²	—	12	2	no	—
21	H(3,𝔽₃)	—	3	1	no	—
22	C₃×C₉	—	12	1	no	—
23	C₃×C₉	C₃×A₄	1	1	yes	characteristic
24	C₂×C₃²	—	3	1	no	—
25	C₂×C₃²	—	9	3	no	—
26	C₂×C₉	—	9	1	no	—
27	C₂²×C₃	—	3	1	no	—
28	C₂²×C₃	—	27	1	no	—
29	C₂²×C₃	#732	1	1	yes	characteristic
30	C₃²	—	9	1	no	—
31	C₃²	C₂²⋊H(3,𝔽₃)	1	1	yes	characteristic
32	C₉	—	3	1	no	—
33	C₉	—	12	3	no	—
34	C₉	—	36	2	no	—
35	C₂×C₃	—	3	1	no	—
36	C₂×C₃	—	9	1	no	—
37	C₂×C₃	—	27	3	no	—
38	C₂²	#6878	1	1	yes	characteristic, complemented, Sylow
39	C₃	—	3	1	no	—
40	C₃	—	27	1	no	—
41	C₃	#66362	1	1	yes	characteristic
42	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.