Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#16862271 | C2 | semidirect |
| 2. C22×#14523498 | C2 | semidirect |
| 3. #22553786 | C2 | semidirect |
| 4. #22553524 | C2 | semidirect |
| 5. #22553504 | C2 | semidirect |
| 6. #22553339 | C2 | semidirect |
| 7. #22553317 | C2 | semidirect |
| 8. #22553308 | C2 | semidirect |
| 9. #535×C131 | C2 | semidirect |
| 12. C2×#14523500 | C22 | semidirect |
| 15. C2×#14523498 | C22 | semidirect |
| 18. C4×D524 | C22 | semidirect |
| 22. C4⋊(C131⋊C8) | C22 | semidirect |
| 23. #16862170 | C22 | semidirect |
| 24. #16862167 | C22 | semidirect |
| 25. #16862167 | C22 | semidirect |
| 28. #127×C131 | C22 | semidirect |
| 29. #124×C131 | C22 | semidirect |
| 36. C2×D524 | D4 | semidirect |
| 121. C131 | #3041 | semidirect |
| 125. #535 | D131 | semidirect |
| 142. #127 | C2×D131 | semidirect |
| 143. #124 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862271 | 2 |
| C22×#14523498 | 2 |
| #22553786 | 2 |
| #22553524 | 2 |
| #22553504 | 2 |
| #22553339 | 2 |
| #22553317 | 2 |
| #22553308 | 2 |
| #535×C131 | 2 |
| #3041 | 131 |