Subgroups — C₃×C₆₄×C₁₂₇ #72201675

Order 24384.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₂×C₁₂₇	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₆×C₁₂₇	C₄	1	1	yes	characteristic
3	C₃×C₈×C₁₂₇	C₈	1	1	yes	characteristic
4	C₆₄×C₁₂₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃₂×C₁₂₇	C₂×C₃	1	1	yes	characteristic
6	C₁₆×C₁₂₇	C₃×C₄	1	1	yes	characteristic
7	C₃×C₄×C₁₂₇	C₁₆	1	1	yes	characteristic
8	C₈×C₁₂₇	C₃×C₈	1	1	yes	characteristic
9	C₂×C₃×C₁₂₇	C₃₂	1	1	yes	characteristic
10	C₄×C₁₂₇	C₃×C₁₆	1	1	yes	characteristic
11	C₃×C₁₂₇	C₆₄	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₁₂₇	C₃×C₃₂	1	1	yes	characteristic
13	C₃×C₆₄	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₁₂₇	C₃×C₆₄	1	1	yes	characteristic, direct product factor, Sylow
15	C₃×C₃₂	C₂×C₁₂₇	1	1	yes	characteristic
16	C₆₄	C₃×C₁₂₇	1	1	yes	characteristic, direct product factor, Sylow
17	C₃×C₁₆	C₄×C₁₂₇	1	1	yes	characteristic
18	C₃₂	C₂×C₃×C₁₂₇	1	1	yes	characteristic
19	C₃×C₈	C₈×C₁₂₇	1	1	yes	characteristic
20	C₁₆	C₃×C₄×C₁₂₇	1	1	yes	characteristic
21	C₃×C₄	C₁₆×C₁₂₇	1	1	yes	characteristic
22	C₈	C₃×C₈×C₁₂₇	1	1	yes	characteristic
23	C₂×C₃	C₃₂×C₁₂₇	1	1	yes	characteristic
24	C₄	C₃×C₁₆×C₁₂₇	1	1	yes	characteristic
25	C₃	C₆₄×C₁₂₇	1	1	yes	characteristic, direct product factor, Sylow
26	C₂	C₃×C₃₂×C₁₂₇	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.