Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
414 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 414 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 |
|---|---|---|
| 2. C2×#16862204 | C2 | semidirect |
| 3. #22553656 | C2 | semidirect |
| 4. #22553655 | C2 | semidirect |
| 5. #22553639 | C2 | semidirect |
| 6. #22553638 | C2 | semidirect |
| 7. #22553355 | C2 | semidirect |
| 8. #22553314 | C2 | semidirect |
| 9. #22553311 | C2 | semidirect |
| 10. #22553275 | C2 | semidirect |
| 11. #428×C131 | C2 | semidirect |
| 30. #16862179 | C22 | semidirect |
| 31. #16862177 | C22 | semidirect |
| 32. #16862171 | C22 | semidirect |
| 33. #16862169 | C22 | semidirect |
| 34. #16862168 | C22 | semidirect |
| 35. #16862166 | C22 | semidirect |
| 41. #107×C131 | C22 | semidirect |
| 42. #106×C131 | C22 | semidirect |
| 152. C131 | #3093 | semidirect |
| 161. #428 | D131 | semidirect |
| 187. #107 | C2×D131 | semidirect |
| 189. #106 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553824 | 2 |
| C2×#16862204 | 2 |
| #22553656 | 2 |
| #22553655 | 2 |
| #22553639 | 2 |
| #22553638 | 2 |
| #22553355 | 2 |
| #22553314 | 2 |
| #22553311 | 2 |
| #22553275 | 2 |
| #428×C131 | 2 |
| #3093 | 131 |