Subgroups — C₃×Dic₂₁ #6983

Order 252.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₇	C₂	1	1	yes	maximal, characteristic
2	Dic₂₁	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×Dic₇	—	3	1	no	maximal
4	C₃²×C₇	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₇	—	2	1	no	—
6	C₂×C₃×C₇	D₃	1	1	yes	characteristic
7	C₂×C₃×C₇	C₂×C₃	1	1	yes	characteristic
8	C₃×Dic₃	—	7	1	no	maximal, Hall
9	Dic₇	—	3	1	no	Hall
10	C₃×C₇	—	2	1	no	—
11	C₃×C₇	Dic₃	1	1	yes	characteristic, complemented
12	C₃×C₇	C₃×C₄	1	1	yes	characteristic, complemented
13	C₂×C₃²	D₇	1	1	yes	characteristic
14	C₂×C₇	C₃×D₃	1	1	yes	characteristic
15	C₃×C₄	—	21	1	no	—
16	Dic₃	—	7	1	no	—
17	C₃²	Dic₇	1	1	yes	characteristic, complemented, Sylow
18	C₇	C₃×Dic₃	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃	—	2	1	no	—
20	C₂×C₃	C₃×D₇	1	1	yes	characteristic
21	C₂×C₃	D₂₁	1	1	yes	characteristic
22	C₄	—	21	1	no	Sylow
23	C₃	—	2	1	no	—
24	C₃	C₃×Dic₇	1	1	yes	characteristic, complemented
25	C₃	Dic₂₁	1	1	yes	characteristic, direct product factor
26	C₂	C₃×D₂₁	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.