Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 133 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. #22553943 | C2 | semidirect |
| 3. #22553615 | C2 | semidirect |
| 4. #22553611 | C2 | semidirect |
| 5. #22553601 | C2 | semidirect |
| 6. #22553591 | C2 | semidirect |
| 7. #22553348 | C2 | semidirect |
| 8. #22553340 | C2 | semidirect |
| 11. #428×C131 | C2 | semidirect |
| 15. #16862245 | C22 | semidirect |
| 17. #16862237 | C22 | semidirect |
| 26. #16862179 | C22 | semidirect |
| 27. #16862179 | C22 | semidirect |
| 28. #16862177 | C22 | semidirect |
| 29. #16862177 | C22 | semidirect |
| 30. Dic131⋊C8 | C22 | semidirect |
| 31. Dic131⋊C8 | C22 | semidirect |
| 39. #107×C131 | C22 | semidirect |
| 40. #106×C131 | C22 | semidirect |
| 45. C2×D524 | Q8 | semidirect |
| 124. C131 | #3081 | semidirect |
| 132. #428 | D131 | semidirect |
| 156. #107 | C2×D131 | semidirect |
| 159. #106 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553943 | 2 |
| #22553786 | 2 |
| #22553615 | 2 |
| #22553611 | 2 |
| #22553601 | 2 |
| #22553591 | 2 |
| #22553348 | 2 |
| #22553340 | 2 |
| #22553318 | 2 |
| C2×#16862166 | 2 |
| #428×C131 | 2 |
| #3081 | 131 |