Subgroups — C₃×C₃₂×C₂₅₁ #72201389

Order 24096.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₆×C₂₅₁	C₂	1	1	yes	maximal, characteristic
2	C₃×C₈×C₂₅₁	C₄	1	1	yes	characteristic
3	C₃₂×C₂₅₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₆×C₂₅₁	C₂×C₃	1	1	yes	characteristic
5	C₃×C₄×C₂₅₁	C₈	1	1	yes	characteristic
6	C₈×C₂₅₁	C₃×C₄	1	1	yes	characteristic
7	C₂×C₃×C₂₅₁	C₁₆	1	1	yes	characteristic
8	C₄×C₂₅₁	C₃×C₈	1	1	yes	characteristic
9	C₃×C₂₅₁	C₃₂	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₂₅₁	C₃×C₁₆	1	1	yes	characteristic
11	C₂₅₁	C₃×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
12	C₃×C₃₂	C₂₅₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₁₆	C₂×C₂₅₁	1	1	yes	characteristic
14	C₃₂	C₃×C₂₅₁	1	1	yes	characteristic, direct product factor, Sylow
15	C₃×C₈	C₄×C₂₅₁	1	1	yes	characteristic
16	C₁₆	C₂×C₃×C₂₅₁	1	1	yes	characteristic
17	C₃×C₄	C₈×C₂₅₁	1	1	yes	characteristic
18	C₈	C₃×C₄×C₂₅₁	1	1	yes	characteristic
19	C₂×C₃	C₁₆×C₂₅₁	1	1	yes	characteristic
20	C₄	C₃×C₈×C₂₅₁	1	1	yes	characteristic
21	C₃	C₃₂×C₂₅₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₃×C₁₆×C₂₅₁	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.