Finite Group DatabasebetaFinite Group DatabasebetaOrder 24576.
5020 conjugacy classes of subgroups.
The subgroup lattice has 308 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C42×C64 | C23×C3 |
| socle, prime radical | C23×C3 | C42×C64 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C82×C128 | C3 | direct (N × H) |
| 19. C3×C8×C128 | C8 | direct (N × H) |
| 48. C8×C128 | C3×C8 | direct (N × H) |
| 108. C3×C128 | C82 | direct (N × H) |
| 148. C3×C82 | C128 | direct (N × H) |
| 178. C128 | C3×C82 | direct (N × H) |
| 218. C82 | C3×C128 | direct (N × H) |
| 264. C3×C8 | C8×C128 | direct (N × H) |
| 293. C8 | C3×C8×C128 | direct (N × H) |
| 304. C3 | C82×C128 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C82×C64 | 2 |
| C3×C4×C8×C128 | 2 |
| C82×C128 | 3 |