Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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. #22554112 | C2 | semidirect |
| 2. C2×#16862274 | C2 | semidirect |
| 3. C2×#16862274 | C2 | semidirect |
| 4. #22554078 | C2 | semidirect |
| 5. #22553583 | C2 | semidirect |
| 6. #22553576 | C2 | semidirect |
| 7. #22553294 | C2 | semidirect |
| 8. C2×#16862162 | C2 | semidirect |
| 9. #430×C131 | C2 | semidirect |
| 14. #16862279 | C22 | semidirect |
| 20. #16862274 | C22 | semidirect |
| 23. C2×#14523502 | C22 | semidirect |
| 25. C2×D1048 | C22 | semidirect |
| 27. #16862252 | C22 | semidirect |
| 30. #16862164 | C22 | semidirect |
| 31. #16862162 | C22 | semidirect |
| 32. #16862162 | C22 | semidirect |
| 36. #108×C131 | C22 | semidirect |
| 147. C131 | #3068 | semidirect |
| 155. #430 | D131 | semidirect |
| 181. #108 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554112 | 2 |
| C2×#16862274 | 2 |
| #22554078 | 2 |
| #22553583 | 2 |
| #22553576 | 2 |
| #22553294 | 2 |
| C2×#16862162 | 2 |
| #430×C131 | 2 |
| #3068 | 131 |