Subgroups — #10590166

Order 576.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊(C₃⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
2	#63540	C₂	1	2	yes	maximal, complemented
3	C₂×C₃²×C₈	C₄	1	1	yes	characteristic
4	C₃⋊(C₃⋊C₁₆)	C₄	1	1	yes	characteristic
5	C₃⋊(C₃⋊C₁₆)	C₂²	1	1	yes	characteristic
6	C₂×C₃⋊C₁₆	—	6	2	no	—
7	C₂×C₃²×C₄	C₈	1	1	yes	characteristic
8	C₃²×C₈	C₈	1	1	yes	characteristic
9	C₃²×C₈	C₂×C₄	1	1	yes	characteristic
10	M₆₄	—	9	1	no	maximal, Sylow
11	C₂×C₃×C₈	—	2	2	no	—
12	C₃⋊C₁₆	—	6	2	no	—
13	C₃⋊C₁₆	—	6	2	no	—
14	C₂²×C₃²	C₁₆	1	1	yes	characteristic
15	C₃²×C₄	C₁₆	1	1	yes	characteristic
16	C₃²×C₄	C₂×C₈	1	1	yes	characteristic
17	C₂×C₁₆	—	9	1	no	—
18	C₃₂	—	9	2	no	—
19	C₂×C₃×C₄	—	2	2	no	—
20	C₃×C₈	—	2	2	no	—
21	C₃×C₈	—	2	2	no	—
22	C₂×C₃²	—	2	1	no	—
23	C₂×C₃²	C₂×C₁₆	1	1	yes	characteristic
24	C₂×C₈	#157	1	1	yes	characteristic
25	C₁₆	—	9	1	no	—
26	C₁₆	—	9	1	no	—
27	C₂²×C₃	—	2	2	no	—
28	C₃×C₄	—	2	2	no	—
29	C₃×C₄	—	2	2	no	—
30	C₃²	M₆₄	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₄	#622	1	1	yes	characteristic
32	C₈	#622	1	1	yes	characteristic
33	C₈	C₂×#157	1	1	yes	characteristic
34	C₂×C₃	—	2	4	no	—
35	C₂×C₃	—	2	2	no	—
36	C₂²	#3708	1	1	yes	characteristic
37	C₄	#3708	1	1	yes	characteristic
38	C₄	C₂×#622	1	1	yes	characteristic
39	C₃	—	2	2	no	—
40	C₂	—	2	1	no	—
41	C₂	C₂×#3708	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. #63540	C₂	semidirect
30. C₃²	M₆₄	semidirect

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