Subgroups — #11757428

Order 972.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#66436	C₃	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₂₇	C₃	1	1	yes	maximal, characteristic, complemented
3	#66353	C₃	1	2	yes	maximal, complemented
4	#6872	—	4	1	no	maximal, Sylow
5	C₂×C₃×C₂₇	—	3	1	no	—
6	C₂²×C₃×C₉	C₃²	1	1	yes	characteristic
7	C₂²⋊H(3,𝔽₃)	C₉	1	1	yes	characteristic
8	#1094	C₉	1	2	yes	—
9	C₉⋊A₄	—	3	2	no	—
10	C₉×A₄	—	3	1	no	—
11	C₂²×C₂₇	—	3	1	no	—
12	C₂²⋊C₂₇	—	3	2	no	—
13	#737	—	4	1	no	—
14	C₂₇⋊C₃	—	4	2	no	—
15	C₃×C₂₇	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	C₂²×C₉	H(3,𝔽₃)	1	1	yes	characteristic
21	C₂²×C₉	3₋¹⁺²	1	2	yes	—
22	C₂²⋊C₉	—	3	2	no	—
23	3₋¹⁺²	—	4	2	no	—
24	3₋¹⁺²	—	12	2	no	—
25	H(3,𝔽₃)	—	4	1	no	—
26	C₃×C₉	—	12	1	no	—
27	C₃×C₉	C₃×A₄	1	1	yes	characteristic
28	C₂₇	—	3	1	no	—
29	C₂₇	—	12	2	no	—
30	C₂×C₃²	—	3	1	no	—
31	C₂×C₉	—	3	2	no	—
32	C₂×C₉	—	3	1	no	—
33	C₂²×C₃	—	3	1	no	—
34	C₂²×C₃	C₃²⋊C₉	1	1	yes	characteristic
35	A₄	—	9	1	no	—
36	C₃²	—	12	1	no	—
37	C₃²	C₉×A₄	1	1	yes	characteristic
38	C₉	—	12	2	no	—
39	C₉	C₉⋊A₄	1	2	yes	—
40	C₉	C₂²⋊H(3,𝔽₃)	1	1	yes	characteristic
41	C₂×C₃	—	3	3	no	—
42	C₂×C₃	—	3	1	no	—
43	C₂²	#6872	1	1	yes	characteristic, complemented, Sylow
44	C₃	—	3	1	no	—
45	C₃	—	36	1	no	—
46	C₃	(C₃×A₄)⋊C₉	1	1	yes	characteristic
47	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.