Subgroups — #66623

Order 336.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₄	C₂	1	1	yes	maximal, characteristic
2	Dic₄₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#1132	—	3	1	no	maximal, Hall
5	C₂×D₂₁	—	2	1	no	—
6	C₃×C₄×C₇	C₂²	1	1	yes	characteristic
7	Dic₂₁	—	2	1	no	—
8	D₂₈	—	3	1	no	—
9	Dic₁₄	—	3	1	no	—
10	C₇×C₈	D₃	1	1	yes	characteristic, complemented
11	#204	—	7	1	no	maximal, Hall
12	C₂×C₃×C₇	D₄	1	1	yes	characteristic
13	D₂₁	—	4	1	no	—
14	C₂×D₇	—	6	1	no	—
15	C₄×C₇	C₂×D₃	1	1	yes	characteristic
16	Dic₇	—	6	1	no	—
17	D₁₂	—	7	1	no	—
18	Dic₆	—	7	1	no	—
19	C₃×C₈	D₇	1	1	yes	characteristic, complemented
20	C₃×C₇	SD₁₆	1	1	yes	characteristic, complemented, Hall
21	SD₁₆	—	21	1	no	Sylow
22	C₂×C₇	D₁₂	1	1	yes	characteristic
23	D₇	—	12	1	no	—
24	C₂×D₃	—	14	1	no	—
25	C₃×C₄	C₂×D₇	1	1	yes	characteristic
26	Dic₃	—	14	1	no	—
27	Q₈	—	21	1	no	—
28	D₄	—	21	1	no	—
29	C₈	D₂₁	1	1	yes	characteristic, complemented
30	C₇	#204	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	D₂₈	1	1	yes	characteristic
32	D₃	—	28	1	no	—
33	C₂²	—	42	1	no	—
34	C₄	—	42	1	no	—
35	C₄	C₂×D₂₁	1	1	yes	characteristic
36	C₃	#1132	1	1	yes	characteristic, complemented, Sylow
37	C₂	—	84	1	no	—
38	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.