Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22554023 | C2 | semidirect |
| 3. #22553660 | C2 | semidirect |
| 4. #22553632 | C2 | semidirect |
| 5. #22553542 | C2 | semidirect |
| 6. #22553513 | C2 | semidirect |
| 7. #22553464 | C2 | semidirect |
| 8. C4×#14523501 | C2 | semidirect |
| 9. #22553377 | C2 | semidirect |
| 10. #102×D131 | C2 | semidirect |
| 11. #476×C131 | C2 | semidirect |
| 14. C2×#14523502 | C22 | semidirect |
| 16. C2×C8×D131 | C22 | semidirect |
| 19. #16862226 | C22 | semidirect |
| 24. C4×Dic262 | C22 | semidirect |
| 27. C4⋊C4×D131 | C22 | semidirect |
| 28. #16862177 | C22 | semidirect |
| 29. #16862169 | C22 | semidirect |
| 30. #16862168 | C22 | semidirect |
| 32. #16862166 | C22 | semidirect |
| 33. #16862166 | C22 | semidirect |
| 34. (C2×D131)⋊C8 | C22 | semidirect |
| 35. C4×C131⋊C8 | C22 | semidirect |
| 36. C4⋊Q8×C131 | C22 | semidirect |
| 38. #106×C131 | C22 | semidirect |
| 39. C4⋊C8×C131 | C22 | semidirect |
| 89. D524 | SD16 | semidirect |
| 136. C131 | #3295 | semidirect |
| 142. #476 | D131 | semidirect |
| 154. C4⋊Q8 | C2×D131 | semidirect |
| 168. #106 | C2×D131 | semidirect |
| 169. C4⋊C8 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554023 | 2 |
| D4×D524 | 2 |
| #22553660 | 2 |
| #22553632 | 2 |
| #22553542 | 2 |
| #22553513 | 2 |
| #22553464 | 2 |
| C4×#14523501 | 2 |
| #22553377 | 2 |
| #102×D131 | 2 |
| #476×C131 | 2 |
| #3295 | 131 |