Subgroups — #216

Order 48.

18 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₈	C₂	1	1	yes	maximal, characteristic
2	Dic₆	C₂	1	1	yes	maximal, characteristic
3	C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	Q₁₆	—	3	1	no	maximal, Sylow
5	C₃×C₄	—	2	1	no	—
6	C₃×C₄	C₂²	1	1	yes	characteristic
7	Dic₃	—	2	1	no	—
8	Q₈	—	3	1	no	—
9	Q₈	D₃	1	1	yes	characteristic
10	C₈	—	3	1	no	—
11	C₂×C₃	D₄	1	1	yes	characteristic
12	C₄	—	2	1	no	—
13	C₄	—	6	1	no	—
14	C₄	C₂×D₃	1	1	yes	characteristic
15	C₃	Q₁₆	1	1	yes	characteristic, complemented, Sylow
16	C₂	#67	1	1	yes	characteristic

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

N	H ≅ G/N	type
15. C₃	Q₁₆	semidirect

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