Subgroups — C₄×D₃×C₇ #4260

Order 168.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×C₇	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₇	—	3	1	no	maximal, Hall
5	C₂×C₃×C₇	C₂²	1	1	yes	characteristic
6	D₃×C₇	C₄	1	2	yes	direct product factor
7	C₂²×C₇	—	3	1	no	—
8	C₄×C₇	—	3	1	no	—
9	C₄×C₇	D₃	1	1	yes	characteristic, direct product factor
10	C₄×D₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₃×C₇	C₂×C₄	1	1	yes	characteristic, complemented, Hall
12	C₂×C₇	—	3	2	no	—
13	C₂×C₇	C₂×D₃	1	1	yes	characteristic
14	C₂×D₃	C₂×C₇	1	1	yes	characteristic
15	C₃×C₄	C₂×C₇	1	1	yes	characteristic, complemented
16	Dic₃	C₂×C₇	1	1	yes	characteristic, complemented
17	C₂×C₄	—	3	1	no	Sylow
18	C₇	C₄×D₃	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₃	C₂²×C₇	1	1	yes	characteristic
20	D₃	C₄×C₇	1	2	yes	direct product factor
21	C₂²	—	3	1	no	—
22	C₄	—	3	1	no	—
23	C₄	D₃×C₇	1	1	yes	characteristic, direct product factor
24	C₃	C₂×C₄×C₇	1	1	yes	characteristic, complemented, Sylow
25	C₂	—	3	2	no	—
26	C₂	C₂×D₃×C₇	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.