Subgroups — #215

Order 48.

20 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, complemented
2	D₁₂	C₂	1	1	yes	maximal, characteristic
3	C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	SD₁₆	—	3	1	no	maximal, Sylow
5	C₂×D₃	—	2	1	no	—
6	C₃×C₄	—	2	1	no	—
7	C₃×C₄	C₂²	1	1	yes	characteristic
8	Q₈	D₃	1	1	yes	characteristic, complemented
9	D₄	—	3	1	no	—
10	C₈	—	3	1	no	—
11	C₂×C₃	D₄	1	1	yes	characteristic
12	D₃	—	4	1	no	—
13	C₂²	—	6	1	no	—
14	C₄	—	2	1	no	—
15	C₄	C₂×D₃	1	1	yes	characteristic
16	C₃	SD₁₆	1	1	yes	characteristic, complemented, Sylow
17	C₂	—	12	1	no	—
18	C₂	#67	1	1	yes	characteristic

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

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