Subgroups — C₃²×D₃×C₇ #67401

Order 378.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₃²×C₇	—	3	1	no	maximal
3	C₃×D₃×C₇	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₇	—	2	4	no	—
5	C₃²×C₇	D₃	1	1	yes	characteristic, direct product factor
6	C₃²×C₇	C₂×C₃	1	4	yes	complemented
7	C₃²×D₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₃×C₇	—	3	4	no	—
9	D₃×C₇	C₃²	1	1	yes	characteristic, direct product factor
10	C₃³	C₂×C₇	1	1	yes	characteristic, complemented, Sylow
11	C₃×C₇	—	2	4	no	—
12	C₃×C₇	C₃×D₃	1	4	yes	direct product factor
13	C₃×C₇	C₂×C₃²	1	1	yes	characteristic, complemented
14	C₂×C₃²	—	3	1	no	—
15	C₃×D₃	C₃×C₇	1	4	yes	direct product factor
16	C₂×C₇	—	3	1	no	Hall
17	C₃²	—	2	4	no	—
18	C₃²	D₃×C₇	1	1	yes	characteristic, direct product factor
19	C₃²	C₂×C₃×C₇	1	4	yes	complemented
20	C₇	C₃²×D₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₂×C₃	—	3	4	no	—
22	D₃	C₃²×C₇	1	1	yes	characteristic, direct product factor
23	C₃	—	2	4	no	—
24	C₃	C₃×D₃×C₇	1	4	yes	direct product factor
25	C₃	C₂×C₃²×C₇	1	1	yes	characteristic, complemented
26	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₇	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₃²×C₇
Frattini	C₁	G
Fitting, socle	C₃³×C₇	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₃²×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.