Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 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. #30656858 | C2 | semidirect |
| 3. #30656849 | C2 | semidirect |
| 4. #30656561 | C2 | semidirect |
| 5. #30656548 | C2 | semidirect |
| 6. #30656514 | C2 | semidirect |
| 7. #361×C257 | C2 | semidirect |
| 11. #22551536 | C4 | semidirect |
| 12. #22551533 | C4 | semidirect |
| 23. Dic1028 | C2×C4 | semidirect |
| 25. D2056 | C2×C4 | semidirect |
| 32. #16861593 | C2×C4 | semidirect |
| 68. C257 | AGL(1,ℤ/16) | semidirect |
| 74. #361 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30657173 | 2 |
| #30656858 | 2 |
| #30656849 | 2 |
| #30656561 | 2 |
| #30656548 | 2 |
| #30656514 | 2 |
| #361×C257 | 2 |
| AGL(1,ℤ/16) | 257 |