Finite Group DatabasebetaFinite Group Databasebeta← C2×C22⋊(C22⋊(C13⋊C3)) #11929344
Order 1248.
296 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C22⋊(C22⋊(C13⋊C3)) |
| commutator, cosocle, hypocenter | C24×C13 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C25×C13 | C3 |
| LCS | G ▷ C24×C13 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22⋊(C22⋊(C13⋊C3)) | C2 | direct (N × H) |
| 2. C25×C13 | C3 | semidirect |
| 6. C24×C13 | C2×C3 | semidirect |
| 12. C23×C13 | A4 | semidirect |
| 19. C22×C13 | C2×A4 | semidirect |
| 22. C25 | C13⋊C3 | semidirect |
| 25. C2×C13 | C22⋊A4 | semidirect |
| 29. C24 | C2×C13⋊C3 | semidirect |
| 30. C13 | C2×C22⋊A4 | semidirect |
| 36. C23 | C22⋊(C13⋊C3) | semidirect |
| 42. C22 | C2×C22⋊(C13⋊C3) | semidirect |
| 46. C2 | C22⋊(C22⋊(C13⋊C3)) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22⋊(C22⋊(C13⋊C3)) | 2 |
| C25×C13 | 3 |
| C2×C22⋊(C13⋊C3) | 4 |
| C2×C22⋊A4 | 13 |