Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
420 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 121 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. #22553647 | C2 | semidirect |
| 5. #22553643 | C2 | semidirect |
| 6. #22553635 | C2 | semidirect |
| 7. #22553623 | C2 | semidirect |
| 8. #22553347 | C2 | semidirect |
| 9. #22553305 | C2 | semidirect |
| 10. C22⋊C8×D131 | C2 | semidirect |
| 11. #481×C131 | C2 | semidirect |
| 30. #16862179 | C22 | semidirect |
| 31. #16862179 | C22 | semidirect |
| 32. #16862178 | C22 | semidirect |
| 33. #16862171 | C22 | semidirect |
| 34. #16862169 | C22 | semidirect |
| 35. #16862167 | C22 | semidirect |
| 40. #106×C131 | C22 | semidirect |
| 41. #102×C131 | C22 | semidirect |
| 143. C131 | #3091 | semidirect |
| 151. #481 | D131 | semidirect |
| 179. #106 | C2×D131 | semidirect |
| 183. #102 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553822 | 2 |
| C2×#16862204 | 2 |
| #22553656 | 2 |
| #22553647 | 2 |
| #22553643 | 2 |
| #22553635 | 2 |
| #22553623 | 2 |
| #22553347 | 2 |
| #22553305 | 2 |
| C22⋊C8×D131 | 2 |
| #481×C131 | 2 |
| #3091 | 131 |