Subgroups — (C₃⋊D₃)⋊D₇ #6998

Order 252.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₂₁	C₂	1	2	yes	maximal, complemented
3	D₃×D₇	—	3	2	no	maximal
4	C₃²×C₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₂₁	D₃	1	2	yes	complemented
6	C₃×D₇	—	3	2	no	—
7	D₃×C₇	—	3	2	no	—
8	D₃×C₇	—	6	1	no	—
9	D₃²	—	7	1	no	maximal, Hall
10	C₂×D₇	—	9	1	no	Hall
11	C₃×C₇	—	2	1	no	—
12	C₃×C₇	C₂×D₃	1	2	yes	complemented
13	C₃⋊D₃	D₇	1	1	yes	characteristic, complemented
14	C₃×D₃	—	7	2	no	—
15	C₂×C₇	—	9	1	no	—
16	D₇	—	3	2	no	—
17	C₂×D₃	—	21	2	no	—
18	C₃²	C₂×D₇	1	1	yes	characteristic, complemented, Sylow
19	C₇	D₃²	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃	—	21	2	no	—
21	D₃	—	3	2	no	—
22	D₃	—	6	1	no	—
23	D₃	—	7	2	no	—
24	C₂²	—	63	1	no	Sylow
25	C₃	—	2	1	no	—
26	C₃	D₃×D₇	1	2	yes	complemented
27	C₂	—	9	1	no	—
28	C₂	—	21	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₇	C₂²
LCS	G ▷ C₃²×C₇
UCS	C₁

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.