Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 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. #22553943 | C2 | semidirect |
| 3. #22553614 | C2 | semidirect |
| 4. #22553610 | C2 | semidirect |
| 5. #22553600 | C2 | semidirect |
| 6. #22553590 | C2 | semidirect |
| 7. #22553352 | C2 | semidirect |
| 8. #22553350 | C2 | semidirect |
| 9. #22553338 | C2 | semidirect |
| 14. #16862245 | C22 | semidirect |
| 16. #16862237 | C22 | semidirect |
| 26. #16862180 | C22 | semidirect |
| 27. #16862180 | C22 | semidirect |
| 28. #16862179 | C22 | semidirect |
| 29. #16862178 | C22 | semidirect |
| 30. #16862178 | C22 | semidirect |
| 31. #16862177 | C22 | semidirect |
| 32. Dic131⋊C8 | C22 | semidirect |
| 33. Dic131⋊C8 | C22 | semidirect |
| 66. C2×D4×C131 | Q8 | semidirect |
| 124. C131 | #3081 | semidirect |
| 170. C2×D4 | Dic262 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553943 | 2 |
| #22553787 | 2 |
| #22553614 | 2 |
| #22553610 | 2 |
| #22553600 | 2 |
| #22553590 | 2 |
| #22553352 | 2 |
| #22553350 | 2 |
| #22553338 | 2 |
| #22553317 | 2 |
| C2×#102×C131 | 2 |
| #3081 | 131 |