Subgroups — #67593

Order 384.

50 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	#4506	C₂	1	2	yes	maximal
3	#1425	—	3	1	no	maximal, Sylow
4	C₂×C₃×C₁₆	C₂²	1	1	yes	characteristic
5	#819	—	2	2	no	—
6	C₃×C₃₂	C₄	1	2	yes	—
7	C₂×C₃₂	D₃	1	1	yes	characteristic
8	#368	—	3	2	no	—
9	C₂×C₃×C₈	D₄	1	1	yes	characteristic
10	#208	—	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	#108	—	6	2	no	—
15	C₃₂	Dic₃	1	2	yes	—
16	C₂×C₃×C₄	D₈	1	1	yes	characteristic
17	C₃×C₈	C₄⋊C₄	1	1	yes	characteristic
18	C₃×C₈	Q₁₆	1	1	yes	characteristic
19	C₃⋊C₈	—	8	2	no	—
20	M₁₆	—	12	2	no	—
21	C₂×C₈	D₁₂	1	1	yes	characteristic
22	C₁₆	Dic₆	1	1	yes	characteristic
23	C₁₆	C₂×Dic₃	1	1	yes	characteristic
24	C₂²×C₃	Q₃₂	1	1	yes	characteristic
25	C₃×C₄	#107	1	1	yes	characteristic
26	C₃×C₄	D₁₆	1	1	yes	characteristic
27	C₂×C₄	D₂₄	1	1	yes	characteristic
28	C₈	—	24	2	no	—
29	C₈	Dic₁₂	1	1	yes	characteristic
30	C₈	C₄⋊Dic₃	1	1	yes	characteristic
31	C₂×C₃	—	2	1	no	—
32	C₂×C₃	#366	1	1	yes	characteristic
33	C₂²	Dic₂₄	1	1	yes	characteristic
34	C₄	D₄₈	1	1	yes	characteristic
35	C₄	#818	1	1	yes	characteristic
36	C₃	#1425	1	1	yes	characteristic, complemented, Sylow
37	C₂	—	2	1	no	—
38	C₂	#4504	1	1	yes	characteristic

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

N	H ≅ G/N	type
36. C₃	#1425	semidirect

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