Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
576 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #30656637 | C2 | semidirect |
| 3. #30656627 | C2 | semidirect |
| 4. #30656622 | C2 | semidirect |
| 5. #30656615 | C2 | semidirect |
| 6. #30656613 | C2 | semidirect |
| 7. #30656608 | C2 | semidirect |
| 8. #30656600 | C2 | semidirect |
| 9. #380×C257 | C2 | semidirect |
| 13. #22551566 | C4 | semidirect |
| 37. C2×C22⋊D257 | C2×C4 | semidirect |
| 44. C4⋊Dic257 | C2×C4 | semidirect |
| 50. #16861595 | C2×C4 | semidirect |
| 54. C22×C4×C257 | C2×C4 | semidirect |
| 129. C257 | #2377 | semidirect |
| 139. #380 | D257 | semidirect |
| 176. C22×C4 | C4×D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551566 | 2 |
| #30656637 | 2 |
| #30656627 | 2 |
| #30656622 | 2 |
| #30656615 | 2 |
| #30656613 | 2 |
| #30656608 | 2 |
| #30656600 | 2 |
| #380×C257 | 2 |
| #2377 | 257 |