Subgroups — C₉⋊C₃₂ #63353

Order 288.

18 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₃⋊C₃₂	—	3	1	no	maximal
3	C₈×C₉	C₄	1	1	yes	characteristic
4	C₃×C₁₆	D₃	1	1	yes	characteristic
5	C₄×C₉	C₈	1	1	yes	characteristic
6	C₃₂	—	9	1	no	Sylow
7	C₃×C₈	Dic₃	1	1	yes	characteristic
8	C₂×C₉	C₁₆	1	1	yes	characteristic
9	C₁₆	D₉	1	1	yes	characteristic
10	C₃×C₄	C₃⋊C₈	1	1	yes	characteristic
11	C₉	C₃₂	1	1	yes	characteristic, complemented, Sylow
12	C₈	Dic₉	1	1	yes	characteristic
13	C₂×C₃	C₃⋊C₁₆	1	1	yes	characteristic
14	C₄	C₉⋊C₈	1	1	yes	characteristic
15	C₃	C₃⋊C₃₂	1	1	yes	characteristic
16	C₂	C₉⋊C₁₆	1	1	yes	characteristic

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

N	H ≅ G/N	type
11. C₉	C₃₂	semidirect

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

subgroup	index
C₉×C₁₆	2
C₃⋊C₃₂	3