Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
528 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 189 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. #22553786 | C2 | semidirect |
| 3. #22553422 | C2 | semidirect |
| 4. C4×#14523498 | C2 | semidirect |
| 5. #22553348 | C2 | semidirect |
| 6. #22553317 | C2 | semidirect |
| 7. #22553316 | C2 | semidirect |
| 8. #22553268 | C2 | semidirect |
| 9. #518×C131 | C2 | semidirect |
| 11. C2×#14523498 | C4 | semidirect |
| 16. C4×D524 | C22 | semidirect |
| 20. #16862179 | C22 | semidirect |
| 21. #16862177 | C22 | semidirect |
| 22. #16862167 | C22 | semidirect |
| 23. #16862166 | C22 | semidirect |
| 24. #16862157 | C22 | semidirect |
| 25. C4×C131⋊C8 | C22 | semidirect |
| 28. C4×D4×C131 | C22 | semidirect |
| 35. C2×D524 | C2×C4 | semidirect |
| 38. #14523498 | C2×C4 | semidirect |
| 39. #14523498 | C2×C4 | semidirect |
| 41. C2×C131⋊C8 | C2×C4 | semidirect |
| 52. C2×D4×C131 | C2×C4 | semidirect |
| 108. C131 | #2948 | semidirect |
| 112. #518 | D131 | semidirect |
| 129. C4×D4 | C2×D131 | semidirect |
| 149. C2×D4 | C4×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523498 | 2 |
| #22553786 | 2 |
| #22553422 | 2 |
| C4×#14523498 | 2 |
| #22553348 | 2 |
| #22553317 | 2 |
| #22553316 | 2 |
| #22553268 | 2 |
| #518×C131 | 2 |
| #2948 | 131 |