Finite Group DatabasebetaFinite Group DatabasebetaOrder 24576.
39964 conjugacy classes of subgroups.
The subgroup lattice has 168 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C128 | C26×C3 |
| socle, prime radical | C26×C3 | C128 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C24×C3×C256 | C2 | direct (N × H) |
| 3. C25×C256 | C3 | direct (N × H) |
| 7. C23×C3×C256 | C22 | direct (N × H) |
| 9. C24×C256 | C2×C3 | direct (N × H) |
| 15. C22×C3×C256 | C23 | direct (N × H) |
| 19. C23×C256 | C22×C3 | direct (N × H) |
| 27. C2×C3×C256 | C24 | direct (N × H) |
| 33. C22×C256 | C23×C3 | direct (N × H) |
| 43. C3×C256 | C25 | direct (N × H) |
| 51. C2×C256 | C24×C3 | direct (N × H) |
| 72. C256 | C25×C3 | direct (N × H) |
| 95. C25×C3 | C256 | direct (N × H) |
| 116. C24×C3 | C2×C256 | direct (N × H) |
| 124. C25 | C3×C256 | direct (N × H) |
| 134. C23×C3 | C22×C256 | direct (N × H) |
| 140. C24 | C2×C3×C256 | direct (N × H) |
| 148. C22×C3 | C23×C256 | direct (N × H) |
| 152. C23 | C22×C3×C256 | direct (N × H) |
| 158. C2×C3 | C24×C256 | direct (N × H) |
| 160. C22 | C23×C3×C256 | direct (N × H) |
| 164. C3 | C25×C256 | direct (N × H) |
| 165. C2 | C24×C3×C256 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×C3×C128 | 2 |
| C24×C3×C256 | 2 |
| C25×C256 | 3 |