Subgroups — C₇⋊(C₉⋊C₈) #92579

Order 504.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₇×C₉	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₇⋊C₈)	—	3	1	no	maximal
3	C₂×C₇×C₉	C₄	1	1	yes	characteristic
4	C₃×C₄×C₇	D₃	1	1	yes	characteristic
5	C₉⋊C₈	—	7	1	no	maximal, Hall
6	C₇×C₉	C₈	1	1	yes	characteristic, complemented, Hall
7	C₇⋊C₈	—	9	1	no	Hall
8	C₂×C₃×C₇	Dic₃	1	1	yes	characteristic
9	C₄×C₉	D₇	1	1	yes	characteristic
10	C₄×C₇	D₉	1	1	yes	characteristic
11	C₃⋊C₈	—	21	1	no	—
12	C₃×C₇	C₃⋊C₈	1	1	yes	characteristic
13	C₂×C₉	Dic₇	1	1	yes	characteristic
14	C₂×C₇	Dic₉	1	1	yes	characteristic
15	C₃×C₄	D₂₁	1	1	yes	characteristic
16	C₉	C₇⋊C₈	1	1	yes	characteristic, complemented, Sylow
17	C₈	—	63	1	no	Sylow
18	C₇	C₉⋊C₈	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃	Dic₂₁	1	1	yes	characteristic
20	C₄	D₆₃	1	1	yes	characteristic
21	C₃	C₃⋊(C₇⋊C₈)	1	1	yes	characteristic
22	C₂	Dic₆₃	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.