Finite Group DatabasebetaFinite Group DatabasebetaOrder 24576.
1308 conjugacy classes of subgroups.
The subgroup lattice has 228 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C256 | C23×C3 |
| socle, prime radical | C23×C3 | C22×C256 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C42×C512 | C3 | direct (N × H) |
| 8. C3×C4×C512 | C4 | direct (N × H) |
| 23. C4×C512 | C3×C4 | direct (N × H) |
| 35. C3×C512 | C42 | direct (N × H) |
| 69. C512 | C3×C42 | direct (N × H) |
| 164. C3×C42 | C512 | direct (N × H) |
| 198. C42 | C3×C512 | direct (N × H) |
| 206. C3×C4 | C4×C512 | direct (N × H) |
| 221. C4 | C3×C4×C512 | direct (N × H) |
| 224. C3 | C42×C512 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C42×C256 | 2 |
| C2×C3×C4×C512 | 2 |
| C42×C512 | 3 |