Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
1412 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1412 conjugacy classes of subgroups — too many to draw. Only its 545 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. #22554148 | C2 | semidirect |
| 2. C2×#16862293 | C2 | semidirect |
| 3. #22554129 | C2 | semidirect |
| 4. #22554124 | C2 | semidirect |
| 5. #22554112 | C2 | semidirect |
| 6. C2×#16862279 | C2 | semidirect |
| 7. #568×C131 | C2 | semidirect |
| 10. #16862293 | C22 | semidirect |
| 11. #16862293 | C22 | semidirect |
| 12. #16862292 | C22 | semidirect |
| 15. C2×#14523513 | C22 | semidirect |
| 18. C22×Dic262 | C22 | semidirect |
| 20. #16862279 | C22 | semidirect |
| 21. #16862279 | C22 | semidirect |
| 22. #16862279 | C22 | semidirect |
| 23. #16862274 | C22 | semidirect |
| 24. #16862274 | C22 | semidirect |
| 25. #16862268 | C22 | semidirect |
| 26. C2×Dic524 | C22 | semidirect |
| 27. C2×#14523502 | C22 | semidirect |
| 29. #131×C131 | C22 | semidirect |
| 30. C2×M16×C131 | C22 | semidirect |
| 112. C131 | #3586 | semidirect |
| 120. #568 | D131 | semidirect |
| 142. #131 | C2×D131 | semidirect |
| 143. C2×M16 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554148 | 2 |
| C2×#16862293 | 2 |
| #22554129 | 2 |
| #22554124 | 2 |
| #22554112 | 2 |
| C2×#16862279 | 2 |
| #568×C131 | 2 |
| #3586 | 131 |