Subgroups — #67592

Order 384.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₃₂	C₂	1	1	yes	maximal, characteristic
2	#4504	C₂	1	2	yes	maximal
3	#1424	—	3	1	no	maximal, Sylow
4	C₂×C₃×C₁₆	C₂²	1	1	yes	characteristic
5	#818	—	2	2	no	—
6	C₃×C₃₂	C₄	1	2	yes	complemented
7	C₂×C₃₂	D₃	1	1	yes	characteristic
8	#366	—	3	2	no	—
9	C₂×C₃×C₈	D₄	1	1	yes	characteristic
10	C₄⋊Dic₃	—	4	2	no	—
11	C₃×C₁₆	C₂×C₄	1	1	yes	characteristic
12	C₃×C₁₆	Q₈	1	1	yes	characteristic
13	C₂×C₁₆	C₂×D₃	1	1	yes	characteristic
14	#107	—	6	2	no	—
15	C₃₂	Dic₃	1	2	yes	complemented
16	C₂×C₃×C₄	D₈	1	1	yes	characteristic
17	C₂×Dic₃	—	8	2	no	—
18	C₃×C₈	C₄⋊C₄	1	1	yes	characteristic
19	C₃×C₈	Q₁₆	1	1	yes	characteristic
20	C₂×C₈	D₁₂	1	1	yes	characteristic
21	C₄⋊C₄	—	12	2	no	—
22	C₁₆	Dic₆	1	1	yes	characteristic
23	C₁₆	C₂×Dic₃	1	1	yes	characteristic
24	C₂²×C₃	D₁₆	1	1	yes	characteristic
25	C₃×C₄	#107	1	1	yes	characteristic
26	C₃×C₄	Q₃₂	1	1	yes	characteristic
27	Dic₃	—	16	2	no	—
28	C₂×C₄	—	24	2	no	—
29	C₂×C₄	D₂₄	1	1	yes	characteristic
30	C₈	Dic₁₂	1	1	yes	characteristic
31	C₈	C₄⋊Dic₃	1	1	yes	characteristic
32	C₂×C₃	#366	1	1	yes	characteristic
33	C₂×C₃	SD₆₄	1	2	yes	—
34	C₂²	D₄₈	1	1	yes	characteristic
35	C₄	—	48	2	no	—
36	C₄	Dic₂₄	1	1	yes	characteristic
37	C₄	#818	1	1	yes	characteristic
38	C₃	#1424	1	1	yes	characteristic, complemented, Sylow
39	C₂	#4449	1	2	yes	—
40	C₂	#4504	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.