Subgroups — C₂×C₃×C₄×C₇ #4269

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×C₄×C₇	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₄×C₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₇	C₄	1	2	yes	direct product factor
5	C₂×C₃×C₇	C₂²	1	1	yes	characteristic
6	C₂²×C₇	C₂×C₃	1	1	yes	characteristic
7	C₄×C₇	C₂×C₃	1	2	yes	direct product factor
8	C₂×C₃×C₄	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₇	C₂×C₄	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₇	C₃×C₄	1	2	yes	direct product factor
11	C₂×C₇	C₂²×C₃	1	1	yes	characteristic
12	C₂²×C₃	C₂×C₇	1	1	yes	characteristic
13	C₃×C₄	C₂×C₇	1	2	yes	direct product factor
14	C₂×C₄	C₃×C₇	1	1	yes	characteristic, direct product factor, Sylow
15	C₇	C₂×C₃×C₄	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₃	C₄×C₇	1	2	yes	direct product factor
17	C₂×C₃	C₂²×C₇	1	1	yes	characteristic
18	C₂²	C₂×C₃×C₇	1	1	yes	characteristic
19	C₄	C₂×C₃×C₇	1	2	yes	direct product factor
20	C₃	C₂×C₄×C₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₂	C₃×C₄×C₇	1	2	yes	direct product factor
22	C₂	C₂²×C₃×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.