Subgroups — C₂³×C₇²×C₆₁ #72201196

Order 23912.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₇×C₆₁	C₇	1	8	yes	maximal, direct product factor
2	C₂²×C₇²×C₆₁	C₂	1	7	yes	maximal, direct product factor
3	C₂×C₇²×C₆₁	C₂²	1	7	yes	direct product factor
4	C₇²×C₆₁	C₂³	1	1	yes	characteristic, direct product factor, Hall
5	C₂²×C₇×C₆₁	C₂×C₇	1	56	yes	direct product factor
6	C₂×C₇×C₆₁	C₂²×C₇	1	56	yes	direct product factor
7	C₂³×C₆₁	C₇²	1	1	yes	characteristic, direct product factor, Hall
8	C₇×C₆₁	C₂³×C₇	1	8	yes	direct product factor
9	C₂³×C₇²	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₆₁	C₂×C₇²	1	7	yes	direct product factor
11	C₂²×C₇²	C₂×C₆₁	1	7	yes	direct product factor
12	C₂×C₆₁	C₂²×C₇²	1	7	yes	direct product factor
13	C₂×C₇²	C₂²×C₆₁	1	7	yes	direct product factor
14	C₆₁	C₂³×C₇²	1	1	yes	characteristic, direct product factor, Sylow
15	C₂³×C₇	C₇×C₆₁	1	8	yes	direct product factor
16	C₇²	C₂³×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
17	C₂²×C₇	C₂×C₇×C₆₁	1	56	yes	direct product factor
18	C₂×C₇	C₂²×C₇×C₆₁	1	56	yes	direct product factor
19	C₂³	C₇²×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
20	C₇	C₂³×C₇×C₆₁	1	8	yes	direct product factor
21	C₂²	C₂×C₇²×C₆₁	1	7	yes	direct product factor
22	C₂	C₂²×C₇²×C₆₁	1	7	yes	direct product factor

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.