Subgroups — C₆₇×Dic₂₁ #19150583

Order 5628.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×C₆₇	C₂	1	1	yes	maximal, characteristic
2	Dic₇×C₆₇	—	3	1	no	maximal, Hall
3	C₃×C₇×C₆₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₆₇	D₃	1	1	yes	characteristic
5	Dic₃×C₆₇	—	7	1	no	maximal, Hall
6	C₇×C₆₇	Dic₃	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₆₇	D₇	1	1	yes	characteristic
8	C₄×C₆₇	—	21	1	no	Hall
9	C₃×C₆₇	Dic₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₆₇	D₂₁	1	1	yes	characteristic
11	Dic₂₁	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₆₇	Dic₂₁	1	1	yes	characteristic, direct product factor, Sylow
13	C₂×C₃×C₇	C₂×C₆₇	1	1	yes	characteristic
14	Dic₇	—	3	1	no	Hall
15	C₃×C₇	C₄×C₆₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₇	D₃×C₆₇	1	1	yes	characteristic
17	Dic₃	—	7	1	no	Hall
18	C₇	Dic₃×C₆₇	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃	D₇×C₆₇	1	1	yes	characteristic
20	C₄	—	21	1	no	Sylow
21	C₃	Dic₇×C₆₇	1	1	yes	characteristic, complemented, Sylow
22	C₂	D₂₁×C₆₇	1	1	yes	characteristic

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