Subgroups — #10590141

Order 576.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#63771	C₂	1	2	yes	maximal
2	C₁₆×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
3	#3788	—	2	2	no	—
4	C₈×C₃⋊D₃	C₂²	1	1	yes	characteristic
5	C₃²×C₁₆	C₄	1	1	yes	characteristic
6	C₃⋊(C₃⋊C₁₆)	C₄	1	1	yes	characteristic
7	D₃×C₁₆	—	6	2	no	—
8	C₄×C₃⋊D₃	D₄	1	1	yes	characteristic
9	#622	—	4	2	no	—
10	C₃²×C₈	C₂×C₄	1	1	yes	characteristic
11	C₃⋊(C₃⋊C₈)	Q₈	1	1	yes	characteristic
12	#368	—	9	1	no	maximal, Sylow
13	D₃×C₈	—	6	2	no	—
14	C₃×C₁₆	—	2	2	no	—
15	C₃⋊C₁₆	—	6	2	no	—
16	C₂×C₃⋊D₃	Q₁₆	1	1	yes	characteristic
17	C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
18	C₃⋊Dic₃	D₈	1	1	yes	characteristic
19	C₂×C₁₆	—	9	1	no	—
20	#108	—	9	2	no	—
21	C₄×D₃	—	6	2	no	—
22	C₃×C₈	—	2	2	no	—
23	C₃⋊C₈	—	6	2	no	—
24	C₂×C₃²	#107	1	1	yes	characteristic
25	C₃⋊D₃	—	2	1	no	—
26	M₁₆	—	18	2	no	—
27	C₂×C₈	—	9	1	no	—
28	C₁₆	—	9	1	no	—
29	C₁₆	#157	1	1	yes	characteristic
30	C₂×D₃	—	6	2	no	—
31	C₃×C₄	—	2	2	no	—
32	Dic₃	—	6	2	no	—
33	C₃²	#368	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₄	—	9	1	no	—
35	C₈	—	9	1	no	—
36	C₈	—	36	2	no	—
37	C₈	C₂×#157	1	1	yes	characteristic
38	C₂×C₃	—	2	2	no	—
39	D₃	—	6	4	no	—
40	C₂²	—	9	1	no	—
41	C₄	—	9	1	no	—
42	C₄	C₄⋊#157	1	1	yes	characteristic
43	C₃	—	2	2	no	—
44	C₂	—	18	1	no	—
45	C₂	#63769	1	1	yes	characteristic

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

N	H ≅ G/N	type
33. C₃²	#368	semidirect

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