Finite Group DatabasebetaFinite Group DatabasebetaOrder 24057.
880 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C92 | C33×C11 |
| socle, prime radical | C33×C11 | C92 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C11×C272 | C3 | direct (N × H) |
| 7. C3×C272 | C11 | direct (N × H) |
| 9. C3×C11×C27 | C27 | direct (N × H) |
| 14. C272 | C3×C11 | direct (N × H) |
| 19. C11×C27 | C3×C27 | direct (N × H) |
| 29. C3×C27 | C11×C27 | direct (N × H) |
| 33. C3×C11 | C272 | direct (N × H) |
| 39. C27 | C3×C11×C27 | direct (N × H) |
| 40. C11 | C3×C272 | direct (N × H) |
| 45. C3 | C11×C272 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×C11×C27 | 3 |
| C11×C272 | 3 |
| C3×C272 | 11 |