Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
420 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 137 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×#16862205 | C2 | semidirect |
| 3. #22553654 | C2 | semidirect |
| 4. #22553648 | C2 | semidirect |
| 5. #22553643 | C2 | semidirect |
| 6. #22553637 | C2 | semidirect |
| 7. #22553631 | C2 | semidirect |
| 8. #22553626 | C2 | semidirect |
| 9. #22553350 | C2 | semidirect |
| 10. #22553309 | C2 | semidirect |
| 11. C2×C22⋊C8×C131 | C2 | semidirect |
| 30. #16862180 | C22 | semidirect |
| 31. #16862180 | C22 | semidirect |
| 32. #16862178 | C22 | semidirect |
| 33. #16862178 | C22 | semidirect |
| 34. #16862171 | C22 | semidirect |
| 35. #16862171 | C22 | semidirect |
| 36. #16862168 | C22 | semidirect |
| 37. #16862168 | C22 | semidirect |
| 143. C131 | #3091 | semidirect |
| 155. C2×C22⋊C8 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553823 | 2 |
| C2×#16862205 | 2 |
| #22553654 | 2 |
| #22553648 | 2 |
| #22553643 | 2 |
| #22553637 | 2 |
| #22553631 | 2 |
| #22553626 | 2 |
| #22553350 | 2 |
| #22553309 | 2 |
| C2×C22⋊C8×C131 | 2 |
| #3091 | 131 |