Subgroups — Dic₃⋊C₈ #814

Order 96.

38 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	C₄×Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₄⋊C₈	—	3	1	no	maximal, Sylow
5	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
6	C₂×Dic₃	C₄	1	1	yes	characteristic
7	C₂×Dic₃	C₄	1	1	yes	characteristic
8	C₃×C₈	—	2	1	no	—
9	C₃⋊C₈	—	2	1	no	—
10	C₂×C₈	—	3	1	no	—
11	C₂×C₈	D₃	1	1	yes	characteristic
12	C₄²	—	3	1	no	—
13	C₂²×C₃	C₂×C₄	1	1	yes	characteristic
14	C₃×C₄	D₄	1	1	yes	characteristic
15	C₃×C₄	Q₈	1	1	yes	characteristic
16	Dic₃	—	2	1	no	—
17	Dic₃	C₈	1	2	yes	complemented
18	C₂×C₄	—	3	1	no	—
19	C₂×C₄	—	3	1	no	—
20	C₂×C₄	C₂×D₃	1	1	yes	characteristic
21	C₈	—	2	1	no	—
22	C₈	—	6	1	no	—
23	C₂×C₃	C₄⋊C₄	1	1	yes	characteristic
24	C₂×C₃	C₂×C₈	1	1	yes	characteristic
25	C₂×C₃	M₁₆	1	1	yes	characteristic
26	C₂²	C₄×D₃	1	1	yes	characteristic
27	C₄	—	3	2	no	—
28	C₄	—	6	1	no	—
29	C₄	Dic₆	1	1	yes	characteristic
30	C₄	#67	1	1	yes	characteristic
31	C₃	C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
32	C₂	D₃×C₈	1	1	yes	characteristic
33	C₂	ΓL(1,𝔽₂₅)	1	1	yes	characteristic
34	C₂	Dic₃⋊C₄	1	1	yes	characteristic

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

N	H ≅ G/N	type
17. Dic₃	C₈	semidirect
31. C₃	C₄⋊C₈	semidirect

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