Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
466 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 145 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. #20299396 | C2 | semidirect |
| 2. C2×#16813650 | C2 | semidirect |
| 3. C2×#16813647 | C2 | semidirect |
| 4. #20298868 | C2 | semidirect |
| 5. #20298861 | C2 | semidirect |
| 6. #20298647 | C2 | semidirect |
| 7. #20298580 | C2 | semidirect |
| 8. C2×#16813538 | C2 | semidirect |
| 9. #568×C113 | C2 | semidirect |
| 13. #16813652 | C22 | semidirect |
| 19. #16813647 | C22 | semidirect |
| 21. C2×#14268636 | C22 | semidirect |
| 23. C2×D904 | C22 | semidirect |
| 27. #16813558 | C22 | semidirect |
| 28. #16813540 | C22 | semidirect |
| 29. #16813538 | C22 | semidirect |
| 30. #16813538 | C22 | semidirect |
| 33. #131×C113 | C22 | semidirect |
| 148. C113 | #3068 | semidirect |
| 152. #568 | D113 | semidirect |
| 175. #131 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299396 | 2 |
| C2×#16813650 | 2 |
| C2×#16813647 | 2 |
| #20298868 | 2 |
| #20298861 | 2 |
| #20298647 | 2 |
| #20298580 | 2 |
| C2×#16813538 | 2 |
| #568×C113 | 2 |
| #3068 | 113 |