Subgroups — C₂×C₃×Dic₇ #4257

Order 168.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₇	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₇	C₂	1	2	yes	maximal, direct product factor
3	C₂×Dic₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₇	C₄	1	2	yes	complemented
5	C₂×C₃×C₇	C₂²	1	1	yes	characteristic
6	C₂²×C₇	C₂×C₃	1	1	yes	characteristic
7	Dic₇	C₂×C₃	1	2	yes	direct product factor
8	C₂×C₃×C₄	—	7	1	no	maximal, Hall
9	C₃×C₇	C₂×C₄	1	1	yes	characteristic, complemented, Hall
10	C₂×C₇	C₃×C₄	1	2	yes	complemented
11	C₂×C₇	C₂²×C₃	1	1	yes	characteristic
12	C₂²×C₃	D₇	1	1	yes	characteristic
13	C₃×C₄	—	7	2	no	—
14	C₂×C₄	—	7	1	no	Sylow
15	C₇	C₂×C₃×C₄	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₃	Dic₇	1	2	yes	direct product factor
17	C₂×C₃	C₂×D₇	1	1	yes	characteristic
18	C₂²	C₃×D₇	1	1	yes	characteristic
19	C₄	—	7	2	no	—
20	C₃	C₂×Dic₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₂	C₃×Dic₇	1	2	yes	direct product factor
22	C₂	C₂×C₃×D₇	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.