Subgroups — #819

Order 96.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₈	C₂	1	1	yes	maximal, characteristic
2	#208	C₂	1	2	yes	maximal
3	#108	—	3	1	no	maximal, Sylow
4	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
5	C₃×C₈	C₄	1	2	yes	—
6	C₃⋊C₈	—	2	2	no	—
7	M₁₆	—	3	2	no	—
8	C₂×C₈	D₃	1	1	yes	characteristic
9	C₂²×C₃	Q₈	1	1	yes	characteristic
10	C₃×C₄	C₂×C₄	1	1	yes	characteristic
11	C₃×C₄	D₄	1	1	yes	characteristic
12	C₂×C₄	C₂×D₃	1	1	yes	characteristic
13	C₈	—	6	2	no	—
14	C₈	Dic₃	1	2	yes	—
15	C₂×C₃	—	2	1	no	—
16	C₂×C₃	C₄⋊C₄	1	1	yes	characteristic
17	C₂²	Dic₆	1	1	yes	characteristic
18	C₄	D₁₂	1	1	yes	characteristic
19	C₄	C₂×Dic₃	1	1	yes	characteristic
20	C₃	#108	1	1	yes	characteristic, complemented, Sylow
21	C₂	—	2	1	no	—
22	C₂	C₄⋊Dic₃	1	1	yes	characteristic

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

N	H ≅ G/N	type
20. C₃	#108	semidirect

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