Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
466 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 1. #22550674 | C2 | semidirect |
| 2. C2×#16861237 | C2 | semidirect |
| 3. C2×#16861234 | C2 | semidirect |
| 4. #22550146 | C2 | semidirect |
| 5. #22550139 | C2 | semidirect |
| 6. #22549925 | C2 | semidirect |
| 7. #22549858 | C2 | semidirect |
| 8. C2×#16861125 | C2 | semidirect |
| 9. #568×C127 | C2 | semidirect |
| 13. #16861239 | C22 | semidirect |
| 19. #16861234 | C22 | semidirect |
| 21. C2×#14523237 | C22 | semidirect |
| 23. C2×D1016 | C22 | semidirect |
| 27. #16861145 | C22 | semidirect |
| 28. #16861127 | C22 | semidirect |
| 29. #16861125 | C22 | semidirect |
| 30. #16861125 | C22 | semidirect |
| 33. #131×C127 | C22 | semidirect |
| 148. C127 | #3068 | semidirect |
| 152. #568 | D127 | semidirect |
| 175. #131 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550674 | 2 |
| C2×#16861237 | 2 |
| C2×#16861234 | 2 |
| #22550146 | 2 |
| #22550139 | 2 |
| #22549925 | 2 |
| #22549858 | 2 |
| C2×#16861125 | 2 |
| #568×C127 | 2 |
| #3068 | 127 |