Subgroups — #11757431

Order 972.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×A₄	C₃	1	1	yes	maximal, characteristic
2	C₂²×C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
3	#66353	C₃	1	2	yes	maximal, complemented
4	#6869	—	4	1	no	maximal, Sylow
5	C₂×C₂₇⋊C₃	—	3	1	no	—
6	C₃²×A₄	C₉	1	1	yes	characteristic
7	C₂²×C₃×C₉	C₃²	1	1	yes	characteristic
8	C₃×C₂²⋊C₉	C₉	1	2	yes	—
9	C₉×A₄	—	3	1	no	—
10	C₉×A₄	—	3	2	no	—
11	C₂²×C₂₇	—	3	1	no	—
12	C₂²⋊C₂₇	—	3	2	no	—
13	C₃²×C₉	—	4	1	no	—
14	C₂₇⋊C₃	—	4	2	no	—
15	C₂₇⋊C₃	A₄	1	1	yes	characteristic, complemented
16	C₂×C₃×C₉	—	3	1	no	—
17	C₂×C₂₇	—	3	3	no	—
18	C₂²×C₃²	C₃×C₉	1	1	yes	characteristic
19	C₃×A₄	—	3	1	no	—
20	C₃×A₄	—	3	3	no	—
21	C₂²×C₉	H(3,𝔽₃)	1	1	yes	characteristic
22	C₂²×C₉	3₋¹⁺²	1	2	yes	—
23	C₂²⋊C₉	—	3	2	no	—
24	C₃³	—	4	1	no	—
25	C₃×C₉	—	4	2	no	—
26	C₃×C₉	—	12	2	no	—
27	C₃×C₉	—	12	1	no	—
28	C₃×C₉	C₃×A₄	1	1	yes	characteristic
29	C₂₇	—	3	1	no	—
30	C₂₇	—	12	2	no	—
31	C₂×C₃²	—	3	1	no	—
32	C₂×C₉	—	3	2	no	—
33	C₂×C₉	—	3	1	no	—
34	C₂²×C₃	—	3	1	no	—
35	C₂²×C₃	C₃²⋊C₉	1	1	yes	characteristic
36	A₄	—	3	3	no	—
37	C₃²	—	12	3	no	—
38	C₃²	—	12	1	no	—
39	C₃²	C₉×A₄	1	1	yes	characteristic
40	C₉	—	12	2	no	—
41	C₉	C₉⋊A₄	1	2	yes	—
42	C₉	C₂²⋊H(3,𝔽₃)	1	1	yes	characteristic
43	C₂×C₃	—	3	1	no	—
44	C₂×C₃	—	9	1	no	—
45	C₂²	#6869	1	1	yes	characteristic, complemented, Sylow
46	C₃	—	3	1	no	—
47	C₃	—	12	3	no	—
48	C₃	(C₃×A₄)⋊C₉	1	1	yes	characteristic
49	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.