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. #22554022 | C2 | semidirect |
| 3. #22553659 | C2 | semidirect |
| 4. #22553632 | C2 | semidirect |
| 5. #22553602 | C2 | semidirect |
| 6. #22553544 | C2 | semidirect |
| 7. #22553512 | C2 | semidirect |
| 8. #22553461 | C2 | semidirect |
| 9. C8×D524 | C2 | semidirect |
| 10. #102×D131 | C2 | semidirect |
| 11. C4×SD16×C131 | C2 | semidirect |
| 14. C2×#14523500 | C22 | semidirect |
| 15. C2×C8×D131 | C22 | semidirect |
| 16. #16862246 | C22 | semidirect |
| 20. #16862222 | C22 | semidirect |
| 26. C4⋊C4×D131 | C22 | semidirect |
| 27. #16862177 | C22 | semidirect |
| 28. C4⋊(C131⋊C8) | C22 | semidirect |
| 29. #16862168 | C22 | semidirect |
| 30. #16862168 | C22 | semidirect |
| 32. #16862166 | C22 | semidirect |
| 33. (C2×D131)⋊C8 | C22 | semidirect |
| 35. C4×Q8×C131 | C22 | semidirect |
| 37. #106×C131 | C22 | semidirect |
| 38. #103×C131 | C22 | semidirect |
| 40. C4×C8×C131 | C22 | semidirect |
| 88. D524 | SD16 | semidirect |
| 136. C131 | #3295 | semidirect |
| 146. C4×SD16 | D131 | semidirect |
| 162. C4×Q8 | C2×D131 | semidirect |
| 168. #106 | C2×D131 | semidirect |
| 170. #103 | C2×D131 | semidirect |
| 177. C4×C8 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554022 | 2 |
| D4×D524 | 2 |
| #22553659 | 2 |
| #22553632 | 2 |
| #22553602 | 2 |
| #22553544 | 2 |
| #22553512 | 2 |
| #22553461 | 2 |
| C8×D524 | 2 |
| #102×D131 | 2 |
| C4×SD16×C131 | 2 |
| #3295 | 131 |