Subgroups — C₂₇×C₃₂ #11720035

Order 864.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₆×C₂₇	C₂	1	1	yes	maximal, characteristic
2	C₉×C₃₂	C₃	1	1	yes	maximal, characteristic
3	C₈×C₂₇	C₄	1	1	yes	characteristic
4	C₉×C₁₆	C₂×C₃	1	1	yes	characteristic
5	C₄×C₂₇	C₈	1	1	yes	characteristic
6	C₃×C₃₂	C₉	1	1	yes	characteristic
7	C₈×C₉	C₃×C₄	1	1	yes	characteristic
8	C₂×C₂₇	C₁₆	1	1	yes	characteristic
9	C₃×C₁₆	C₂×C₉	1	1	yes	characteristic
10	C₄×C₉	C₃×C₈	1	1	yes	characteristic
11	C₃₂	C₂₇	1	1	yes	characteristic, direct product factor, Sylow
12	C₂₇	C₃₂	1	1	yes	characteristic, direct product factor, Sylow
13	C₃×C₈	C₄×C₉	1	1	yes	characteristic
14	C₂×C₉	C₃×C₁₆	1	1	yes	characteristic
15	C₁₆	C₂×C₂₇	1	1	yes	characteristic
16	C₃×C₄	C₈×C₉	1	1	yes	characteristic
17	C₉	C₃×C₃₂	1	1	yes	characteristic
18	C₈	C₄×C₂₇	1	1	yes	characteristic
19	C₂×C₃	C₉×C₁₆	1	1	yes	characteristic
20	C₄	C₈×C₂₇	1	1	yes	characteristic
21	C₃	C₉×C₃₂	1	1	yes	characteristic
22	C₂	C₁₆×C₂₇	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
11. C₃₂	C₂₇	direct (N × H)
12. C₂₇	C₃₂	direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₆×C₂₇	2
C₉×C₃₂	3