Finite Group DatabasebetaFinite Group DatabasebetaOrder 24576.
1052 conjugacy classes of subgroups.
The subgroup lattice has 136 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C512 | C24×C3 |
| socle, prime radical | C24×C3 | C512 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C3×C1024 | C2 | direct (N × H) |
| 3. C23×C1024 | C3 | direct (N × H) |
| 7. C2×C3×C1024 | C22 | direct (N × H) |
| 9. C22×C1024 | C2×C3 | direct (N × H) |
| 15. C3×C1024 | C23 | direct (N × H) |
| 19. C2×C1024 | C22×C3 | direct (N × H) |
| 32. C1024 | C23×C3 | direct (N × H) |
| 103. C23×C3 | C1024 | direct (N × H) |
| 116. C22×C3 | C2×C1024 | direct (N × H) |
| 120. C23 | C3×C1024 | direct (N × H) |
| 126. C2×C3 | C22×C1024 | direct (N × H) |
| 128. C22 | C2×C3×C1024 | direct (N × H) |
| 132. C3 | C23×C1024 | direct (N × H) |
| 133. C2 | C22×C3×C1024 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×C512 | 2 |
| C22×C3×C1024 | 2 |
| C23×C1024 | 3 |