Subgroups — D₁₆₈ #66624

Order 336.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₄	C₂	1	2	yes	maximal, complemented
2	C₃×C₇×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	D₅₆	—	3	1	no	maximal, Hall
4	C₂×D₂₁	—	2	2	no	—
5	C₃×C₄×C₇	C₂²	1	1	yes	characteristic
6	D₂₈	—	3	2	no	—
7	C₇×C₈	D₃	1	1	yes	characteristic, complemented
8	D₂₄	—	7	1	no	maximal, Hall
9	C₂×C₃×C₇	D₄	1	1	yes	characteristic
10	D₂₁	—	4	2	no	—
11	C₂×D₇	—	6	2	no	—
12	C₄×C₇	C₂×D₃	1	1	yes	characteristic
13	D₁₂	—	7	2	no	—
14	C₃×C₈	D₇	1	1	yes	characteristic, complemented
15	C₃×C₇	D₈	1	1	yes	characteristic, complemented, Hall
16	D₈	—	21	1	no	Sylow
17	C₂×C₇	D₁₂	1	1	yes	characteristic
18	D₇	—	12	2	no	—
19	C₂×D₃	—	14	2	no	—
20	C₃×C₄	C₂×D₇	1	1	yes	characteristic
21	D₄	—	21	2	no	—
22	C₈	D₂₁	1	1	yes	characteristic, complemented
23	C₇	D₂₄	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₃	D₂₈	1	1	yes	characteristic
25	D₃	—	28	2	no	—
26	C₂²	—	42	2	no	—
27	C₄	C₂×D₂₁	1	1	yes	characteristic
28	C₃	D₅₆	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	84	2	no	—
30	C₂	D₈₄	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.