Subgroups — C₇×C₃⋊D₉ #67387

Order 378.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₃⋊D₃	—	3	1	no	maximal
3	C₇×D₉	—	3	3	no	maximal
4	C₃²×C₇	D₃	1	1	yes	characteristic
5	C₇×C₉	D₃	1	3	yes	complemented
6	C₃⋊D₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	D₃×C₇	—	9	3	no	—
8	D₃×C₇	—	9	1	no	—
9	C₃×C₉	C₂×C₇	1	1	yes	characteristic, complemented, Sylow
10	C₃×C₇	D₉	1	3	yes	complemented
11	C₃×C₇	C₃⋊D₃	1	1	yes	characteristic
12	C₃⋊D₃	—	3	1	no	—
13	D₉	—	3	3	no	—
14	C₂×C₇	—	27	1	no	Hall
15	C₃²	D₃×C₇	1	1	yes	characteristic
16	C₉	D₃×C₇	1	3	yes	complemented
17	C₇	C₃⋊D₉	1	1	yes	characteristic, direct product factor, Sylow
18	D₃	—	9	3	no	—
19	D₃	—	9	1	no	—
20	C₃	C₇×D₉	1	3	yes	complemented
21	C₃	C₇×C₃⋊D₃	1	1	yes	characteristic
22	C₂	—	27	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	C₃⋊D₉
commutator, cosocle, hypocenter	C₃×C₉	C₂×C₇
Frattini	C₃	C₇×C₃⋊D₃
Fitting	C₃×C₇×C₉	C₂
socle	C₃²×C₇	D₃
LCS	G ▷ C₃×C₉
UCS	C₁ ◁ C₇

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.