Subgroups — #10589386

Order 576.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₁₆	C₂	1	1	yes	maximal, characteristic
2	#63628	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊(C₃⋊C₃₂)	C₂	1	1	yes	maximal, characteristic, complemented
4	#4520	—	3	4	no	maximal
5	C₃²×D₈	—	2	1	no	—
6	#3746	—	2	1	no	—
7	C₃²×C₁₆	C₂²	1	1	yes	characteristic
8	C₃×D₁₆	D₃	1	4	yes	—
9	Dic₂₄	—	3	4	no	—
10	C₃⋊C₃₂	—	3	4	no	—
11	C₃²×D₄	—	4	1	no	—
12	#634	—	4	1	no	—
13	C₃²×C₈	D₄	1	1	yes	characteristic
14	SD₆₄	—	9	1	no	Sylow
15	C₃×D₈	—	2	4	no	—
16	Dic₁₂	—	6	4	no	—
17	C₃×C₁₆	C₂×D₃	1	4	yes	—
18	C₂²×C₃²	—	8	1	no	—
19	C₃²×C₄	D₈	1	1	yes	characteristic
20	C₃⋊Dic₃	—	8	1	no	—
21	Q₃₂	—	9	1	no	—
22	D₁₆	C₃⋊D₃	1	1	yes	characteristic
23	C₃₂	—	9	1	no	—
24	C₃×D₄	—	4	4	no	—
25	Dic₆	—	12	4	no	—
26	C₃×C₈	#67	1	4	yes	—
27	C₂×C₃²	—	16	1	no	—
28	C₂×C₃²	D₁₆	1	1	yes	characteristic
29	Q₁₆	—	18	1	no	—
30	D₈	—	2	1	no	—
31	C₁₆	C₂×C₃⋊D₃	1	1	yes	characteristic
32	C₂²×C₃	—	8	4	no	—
33	C₃×C₄	#213	1	4	yes	—
34	Dic₃	—	24	4	no	—
35	C₃²	SD₆₄	1	1	yes	characteristic, complemented, Sylow
36	Q₈	—	36	1	no	—
37	D₄	—	4	1	no	—
38	C₈	#638	1	1	yes	characteristic
39	C₂×C₃	—	16	4	no	—
40	C₂×C₃	#826	1	4	yes	—
41	C₂²	—	8	1	no	—
42	C₄	—	72	1	no	—
43	C₄	#3753	1	1	yes	characteristic
44	C₃	#4520	1	4	yes	complemented
45	C₂	—	16	1	no	—
46	C₂	#63653	1	1	yes	characteristic

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.