Subgroups — C₁₇×C₂₃×C₃₂ #72190855

Order 12512.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₆×C₁₇×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₈×C₁₇×C₂₃	C₄	1	1	yes	characteristic
3	C₄×C₁₇×C₂₃	C₈	1	1	yes	characteristic
4	C₂×C₁₇×C₂₃	C₁₆	1	1	yes	characteristic
5	C₂₃×C₃₂	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₇×C₃₂	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₇×C₂₃	C₃₂	1	1	yes	characteristic, direct product factor, Hall
8	C₁₆×C₂₃	C₂×C₁₇	1	1	yes	characteristic
9	C₁₆×C₁₇	C₂×C₂₃	1	1	yes	characteristic
10	C₈×C₂₃	C₄×C₁₇	1	1	yes	characteristic
11	C₈×C₁₇	C₄×C₂₃	1	1	yes	characteristic
12	C₄×C₂₃	C₈×C₁₇	1	1	yes	characteristic
13	C₄×C₁₇	C₈×C₂₃	1	1	yes	characteristic
14	C₂×C₂₃	C₁₆×C₁₇	1	1	yes	characteristic
15	C₂×C₁₇	C₁₆×C₂₃	1	1	yes	characteristic
16	C₃₂	C₁₇×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
17	C₂₃	C₁₇×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
18	C₁₇	C₂₃×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
19	C₁₆	C₂×C₁₇×C₂₃	1	1	yes	characteristic
20	C₈	C₄×C₁₇×C₂₃	1	1	yes	characteristic
21	C₄	C₈×C₁₇×C₂₃	1	1	yes	characteristic
22	C₂	C₁₆×C₁₇×C₂₃	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.