Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
492 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 127 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. #22553863 | C2 | semidirect |
| 2. C4×D4×D131 | C2 | semidirect |
| 3. #22553627 | C2 | semidirect |
| 4. #22553589 | C2 | semidirect |
| 5. #22553508 | C2 | semidirect |
| 6. #22553507 | C2 | semidirect |
| 7. #22553447 | C2 | semidirect |
| 8. #22553394 | C2 | semidirect |
| 9. #22553392 | C2 | semidirect |
| 10. #22553364 | C2 | semidirect |
| 11. #474×C131 | C2 | semidirect |
| 17. #16862243 | C22 | semidirect |
| 25. #16862208 | C22 | semidirect |
| 31. #16862179 | C22 | semidirect |
| 32. C4⋊(C131⋊C8) | C22 | semidirect |
| 33. #16862168 | C22 | semidirect |
| 35. #16862166 | C22 | semidirect |
| 37. C8×Dic131 | C22 | semidirect |
| 38. C4⋊Q8×C131 | C22 | semidirect |
| 40. #107×C131 | C22 | semidirect |
| 41. C4⋊C8×C131 | C22 | semidirect |
| 96. D524 | #41 | semidirect |
| 110. C4×D131 | D8 | semidirect |
| 115. D4×C131 | #41 | semidirect |
| 154. C131 | #3100 | semidirect |
| 160. #474 | D131 | semidirect |
| 172. C4⋊Q8 | C2×D131 | semidirect |
| 189. #107 | C2×D131 | semidirect |
| 191. C4⋊C8 | C2×D131 | semidirect |
| 256. D4 | #14523514 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553863 | 2 |
| C4×D4×D131 | 2 |
| #22553627 | 2 |
| #22553589 | 2 |
| #22553508 | 2 |
| #22553507 | 2 |
| #22553447 | 2 |
| #22553394 | 2 |
| #22553392 | 2 |
| #22553364 | 2 |
| #474×C131 | 2 |
| #3100 | 131 |