Subgroups — C₂×C₉×D₇ #6973

Order 252.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×D₇	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×D₇	C₃	1	1	yes	maximal, characteristic
4	C₇×C₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₇	C₂×C₃	1	1	yes	characteristic
6	C₃×D₇	C₂×C₃	1	2	yes	—
7	C₂²×C₉	—	7	1	no	maximal, Hall
8	C₂×D₇	C₉	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₇	C₂²×C₃	1	1	yes	characteristic
10	C₂×C₉	—	7	2	no	—
11	C₂×C₉	D₇	1	1	yes	characteristic, direct product factor
12	C₂×C₇	C₂×C₉	1	1	yes	characteristic, complemented
13	D₇	C₂×C₉	1	2	yes	direct product factor
14	C₂²×C₃	—	7	1	no	—
15	C₉	C₂×D₇	1	1	yes	characteristic, direct product factor, Sylow
16	C₇	C₂²×C₉	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₃	—	7	2	no	—
18	C₂×C₃	C₃×D₇	1	1	yes	characteristic
19	C₂²	—	7	1	no	Sylow
20	C₃	C₂×C₃×D₇	1	1	yes	characteristic
21	C₂	—	7	2	no	—
22	C₂	C₉×D₇	1	1	yes	characteristic, direct product factor

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.