Finite Group Databasebeta

← C₂×C₃³×C₇ #67407

Subgroups — C₂×C₃³×C₇ #67407

Order 378.

112 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, direct product factor, Hall
2	C₂×C₃²×C₇	C₃	1	13	yes	maximal, direct product factor
3	C₃²×C₇	C₂×C₃	1	13	yes	direct product factor
4	C₂×C₃³	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₇	C₃²	1	13	yes	direct product factor
6	C₃³	C₂×C₇	1	1	yes	characteristic, direct product factor, Sylow
7	C₃×C₇	C₂×C₃²	1	13	yes	direct product factor
8	C₂×C₃²	C₃×C₇	1	13	yes	direct product factor
9	C₂×C₇	C₃³	1	1	yes	characteristic, direct product factor, Hall
10	C₃²	C₂×C₃×C₇	1	13	yes	direct product factor
11	C₇	C₂×C₃³	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₃	C₃²×C₇	1	13	yes	direct product factor
13	C₃	C₂×C₃²×C₇	1	13	yes	direct product factor
14	C₂	C₃³×C₇	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃³×C₇	C₂	direct (N × H)
2. C₂×C₃²×C₇	C₃	direct (N × H)
3. C₃²×C₇	C₂×C₃	direct (N × H)
4. C₂×C₃³	C₇	direct (N × H)
5. C₂×C₃×C₇	C₃²	direct (N × H)
6. C₃³	C₂×C₇	direct (N × H)
7. C₃×C₇	C₂×C₃²	direct (N × H)
8. C₂×C₃²	C₃×C₇	direct (N × H)
9. C₂×C₇	C₃³	direct (N × H)
10. C₃²	C₂×C₃×C₇	direct (N × H)
11. C₇	C₂×C₃³	direct (N × H)
12. C₂×C₃	C₃²×C₇	direct (N × H)
13. C₃	C₂×C₃²×C₇	direct (N × H)
14. C₂	C₃³×C₇	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃³×C₇	2
C₂×C₃²×C₇	3
C₂×C₃³	7