Finite Group Databasebeta

← C₂×C₃×C₆₇² #41002221

Subgroups — C₂×C₃×C₆₇² #41002221

Order 26934.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₆₇²	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₆₇²	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₆₇²	C₂×C₃	1	1	yes	characteristic, direct product factor, Sylow
4	C₂×C₃×C₆₇	C₆₇	1	68	yes	maximal, direct product factor
5	C₃×C₆₇	C₂×C₆₇	1	68	yes	direct product factor
6	C₂×C₆₇	C₃×C₆₇	1	68	yes	direct product factor
7	C₆₇	C₂×C₃×C₆₇	1	68	yes	direct product factor
8	C₂×C₃	C₆₇²	1	1	yes	characteristic, direct product factor, Hall
9	C₃	C₂×C₆₇²	1	1	yes	characteristic, direct product factor, Sylow
10	C₂	C₃×C₆₇²	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. C₃×C₆₇²	C₂	direct (N × H)
2. C₂×C₆₇²	C₃	direct (N × H)
3. C₆₇²	C₂×C₃	direct (N × H)
4. C₂×C₃×C₆₇	C₆₇	direct (N × H)
5. C₃×C₆₇	C₂×C₆₇	direct (N × H)
6. C₂×C₆₇	C₃×C₆₇	direct (N × H)
7. C₆₇	C₂×C₃×C₆₇	direct (N × H)
8. C₂×C₃	C₆₇²	direct (N × H)
9. C₃	C₂×C₆₇²	direct (N × H)
10. C₂	C₃×C₆₇²	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₆₇²	2
C₂×C₆₇²	3
C₂×C₃×C₆₇	67