Finite Group DatabasebetaFinite Group Databasebeta← C7×C22⋊((C43⋊C3)⋊C7) #38760397
Order 25284.
100 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C22⋊((C43⋊C3)⋊C7) |
| commutator, cosocle, hypocenter | C22×C43 | C3×C72 |
| Frattini | C1 | G |
| Fitting, socle | C22×C7×C43 | C3×C7 |
| LCS | G ▷ C22×C43 | |
| UCS | C1 ◁ C7 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C7×C43⋊C7 | C3 | semidirect |
| 4. C7×C22⋊(C43⋊C3) | C7 | semidirect |
| 5. C22⋊((C43⋊C3)⋊C7) | C7 | direct (N × H) |
| 6. C7×C43⋊C7 | A4 | semidirect |
| 7. C22×C7×C43 | C3×C7 | semidirect |
| 8. C22×C43⋊C7 | C3×C7 | semidirect |
| 14. C22⋊(C43⋊C3) | C72 | semidirect |
| 15. C7×C43 | C7×A4 | semidirect |
| 16. C43⋊C7 | C7×A4 | semidirect |
| 18. C22×C43 | C3×C72 | semidirect |
| 26. C43 | C72×A4 | semidirect |
| 28. C22×C7 | (C43⋊C3)⋊C7 | semidirect |
| 35. C7 | C22⋊((C43⋊C3)⋊C7) | direct (N × H) |
| 36. C22 | C7×(C43⋊C3)⋊C7 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×C43⋊C7 | 3 |
| C7×(C43⋊C3)⋊C7 | 4 |
| C7×C22⋊(C43⋊C3) | 7 |
| C22⋊((C43⋊C3)⋊C7) | 7 |
| C72×A4 | 43 |