Subgroups — #67582

Order 384.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#368	C₂	1	1	yes	maximal, characteristic
2	#4505	C₂	1	1	yes	maximal, characteristic
3	#4499	C₂	1	1	yes	maximal, characteristic
4	#1426	—	3	1	no	maximal, Sylow
5	C₂×C₃×C₁₆	C₂²	1	1	yes	characteristic
6	C₃×#108	—	2	1	no	—
7	#818	—	2	1	no	—
8	C₃⋊C₃₂	C₄	1	2	yes	complemented
9	M₆₄	—	3	1	no	—
10	#368	D₃	1	1	yes	characteristic
11	#367	—	3	1	no	—
12	C₃×M₁₆	—	4	1	no	—
13	C₂×C₃×C₈	D₄	1	1	yes	characteristic
14	C₄⋊Dic₃	—	4	1	no	—
15	C₃×C₁₆	C₂×C₄	1	1	yes	characteristic
16	C₃×C₁₆	Q₈	1	1	yes	characteristic
17	C₂×C₁₆	C₂×D₃	1	1	yes	characteristic
18	#108	—	2	1	no	—
19	#107	—	6	1	no	—
20	C₃₂	—	3	2	no	—
21	C₂×C₃×C₄	D₈	1	1	yes	characteristic
22	C₂×Dic₃	—	8	1	no	—
23	C₃×C₈	—	8	1	no	—
24	C₃×C₈	C₄⋊C₄	1	1	yes	characteristic
25	C₃×C₈	Q₁₆	1	1	yes	characteristic
26	M₁₆	—	4	1	no	—
27	C₂×C₈	#67	1	1	yes	characteristic
28	C₄⋊C₄	—	12	1	no	—
29	C₁₆	Dic₆	1	1	yes	characteristic
30	C₁₆	C₄×D₃	1	1	yes	characteristic
31	C₂²×C₃	SD₃₂	1	1	yes	characteristic
32	C₃×C₄	#107	1	1	yes	characteristic
33	C₃×C₄	SD₃₂	1	1	yes	characteristic
34	Dic₃	—	16	1	no	—
35	C₂×C₄	—	24	1	no	—
36	C₂×C₄	#213	1	1	yes	characteristic
37	C₈	—	8	1	no	—
38	C₈	Dic₃⋊C₄	1	1	yes	characteristic
39	C₈	#216	1	1	yes	characteristic
40	C₂×C₃	—	2	1	no	—
41	C₂×C₃	#367	1	1	yes	characteristic
42	C₂²	#828	1	1	yes	characteristic
43	C₄	—	48	1	no	—
44	C₄	#807	1	1	yes	characteristic
45	C₄	#827	1	1	yes	characteristic
46	C₃	#1426	1	1	yes	characteristic, complemented, Sylow
47	C₂	—	2	1	no	—
48	C₂	#4490	1	1	yes	characteristic

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

N	H ≅ G/N	type
8. C₃⋊C₃₂	C₄	semidirect
46. C₃	#1426	semidirect

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