Finite Group DatabasebetaFinite Group DatabasebetaOrder 32512.
3246 conjugacy classes of subgroups.
The subgroup lattice has 384 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C25×C127 | C23 |
| commutator | C22 | C22×C42×C127 |
| Frattini, cosocle | C24 | C24×C127 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C25×C127 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C127×#1434 | C2 | direct (N × H) |
| 11. C22×C42×C127 | C4 | semidirect |
| 15. C2×#95×C127 | C4 | semidirect |
| 46. C2×C42×C127 | C2×C4 | semidirect |
| 49. #95×C127 | C2×C4 | semidirect |
| 181. C2×#1434 | C127 | direct (N × H) |
| 182. C2×C127 | #1434 | direct (N × H) |
| 196. #1434 | C2×C127 | direct (N × H) |
| 197. C127 | C2×#1434 | direct (N × H) |
| 203. C22×C42 | C4×C127 | semidirect |
| 207. C2×#95 | C4×C127 | semidirect |
| 238. C2×C42 | C2×C4×C127 | semidirect |
| 241. #95 | C2×C4×C127 | semidirect |
| 373. C2 | C127×#1434 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C42×C127 | 2 |
| C22×#95×C127 | 2 |
| C127×#1434 | 2 |
| C2×#1434 | 127 |