Subgroups — D₈₄ #4266

Order 168.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₁	C₂	1	2	yes	maximal, complemented
2	C₃×C₄×C₇	C₂	1	1	yes	maximal, characteristic, complemented
3	D₂₈	—	3	1	no	maximal, Hall
4	C₂×C₃×C₇	C₂²	1	1	yes	characteristic
5	D₂₁	—	2	2	no	—
6	C₂×D₇	—	3	2	no	—
7	C₄×C₇	D₃	1	1	yes	characteristic, complemented
8	D₁₂	—	7	1	no	maximal, Hall
9	C₃×C₇	D₄	1	1	yes	characteristic, complemented, Hall
10	C₂×C₇	C₂×D₃	1	1	yes	characteristic
11	D₇	—	6	2	no	—
12	C₂×D₃	—	7	2	no	—
13	C₃×C₄	D₇	1	1	yes	characteristic, complemented
14	D₄	—	21	1	no	Sylow
15	C₇	D₁₂	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₃	C₂×D₇	1	1	yes	characteristic
17	D₃	—	14	2	no	—
18	C₂²	—	21	2	no	—
19	C₄	D₂₁	1	1	yes	characteristic, complemented
20	C₃	D₂₈	1	1	yes	characteristic, complemented, Sylow
21	C₂	—	42	2	no	—
22	C₂	C₂×D₂₁	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.