Subgroups — C₇×C₉⋊C₈ #92577

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	C₇×C₃⋊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	C₇	1	1	yes	maximal, characteristic, direct product factor, 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	C₂×C₇	1	1	yes	characteristic
10	C₄×C₇	D₉	1	1	yes	characteristic
11	C₃⋊C₈	—	3	1	no	—
12	C₃×C₇	C₃⋊C₈	1	1	yes	characteristic
13	C₂×C₉	C₄×C₇	1	1	yes	characteristic
14	C₂×C₇	Dic₉	1	1	yes	characteristic
15	C₃×C₄	D₃×C₇	1	1	yes	characteristic
16	C₉	C₇×C₈	1	1	yes	characteristic, complemented, Sylow
17	C₈	—	9	1	no	Sylow
18	C₇	C₉⋊C₈	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₃	C₇×Dic₃	1	1	yes	characteristic
20	C₄	C₇×D₉	1	1	yes	characteristic
21	C₃	C₇×C₃⋊C₈	1	1	yes	characteristic
22	C₂	C₇×Dic₉	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.