Subgroups — Dic₃⋊C₄ #210

Order 48.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂×Dic₃	C₂	1	1	yes	maximal, characteristic
4	C₄⋊C₄	—	3	1	no	maximal, Sylow
5	C₂²×C₃	C₂²	1	1	yes	characteristic
6	C₃×C₄	—	2	1	no	—
7	Dic₃	—	2	1	no	—
8	Dic₃	C₄	1	2	yes	complemented
9	C₂×C₄	—	3	1	no	—
10	C₂×C₄	—	3	1	no	—
11	C₂×C₄	D₃	1	1	yes	characteristic
12	C₂×C₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₃	D₄	1	1	yes	characteristic
14	C₂×C₃	Q₈	1	1	yes	characteristic
15	C₂²	C₂×D₃	1	1	yes	characteristic
16	C₄	—	2	1	no	—
17	C₄	—	3	2	no	—
18	C₄	—	6	1	no	—
19	C₃	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
20	C₂	Dic₆	1	1	yes	characteristic
21	C₂	C₄×D₃	1	1	yes	characteristic
22	C₂	#67	1	1	yes	characteristic

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

N	H ≅ G/N	type
8. Dic₃	C₄	semidirect
19. C₃	C₄⋊C₄	semidirect

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