Subgroups — #800

Order 96.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₂	C₂	1	1	yes	maximal, characteristic, complemented
2	D₂₄	C₂	1	1	yes	maximal, characteristic
3	C₃×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	SD₃₂	—	3	1	no	maximal, Sylow
5	D₁₂	—	2	1	no	—
6	Dic₆	—	2	1	no	—
7	C₃×C₈	C₂²	1	1	yes	characteristic
8	Q₁₆	—	3	1	no	—
9	D₈	—	3	1	no	—
10	C₁₆	D₃	1	1	yes	characteristic, complemented
11	C₂×D₃	—	4	1	no	—
12	C₃×C₄	D₄	1	1	yes	characteristic
13	Dic₃	—	4	1	no	—
14	Q₈	—	6	1	no	—
15	D₄	—	6	1	no	—
16	C₈	C₂×D₃	1	1	yes	characteristic
17	C₂×C₃	D₈	1	1	yes	characteristic
18	D₃	—	8	1	no	—
19	C₂²	—	12	1	no	—
20	C₄	—	12	1	no	—
21	C₄	D₁₂	1	1	yes	characteristic
22	C₃	SD₃₂	1	1	yes	characteristic, complemented, Sylow
23	C₂	—	24	1	no	—
24	C₂	D₂₄	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.