Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 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. C2×#16813648 | C2 | semidirect |
| 2. C2×#16813629 | C2 | semidirect |
| 3. #20299176 | C2 | semidirect |
| 4. #20298849 | C2 | semidirect |
| 5. #20298842 | C2 | semidirect |
| 6. #20298832 | C2 | semidirect |
| 7. #20298825 | C2 | semidirect |
| 8. #20298641 | C2 | semidirect |
| 9. #20298592 | C2 | semidirect |
| 10. C2×#16813543 | C2 | semidirect |
| 11. #535×C113 | C2 | semidirect |
| 18. C2×#14268631 | C22 | semidirect |
| 20. C22×#11744751 | C22 | semidirect |
| 21. #16813601 | C22 | semidirect |
| 23. #16813596 | C22 | semidirect |
| 27. #16813555 | C22 | semidirect |
| 28. #16813553 | C22 | semidirect |
| 29. #16813545 | C22 | semidirect |
| 30. #16813545 | C22 | semidirect |
| 33. #16813542 | C22 | semidirect |
| 34. #16813542 | C22 | semidirect |
| 54. #14268631 | D4 | semidirect |
| 152. C113 | #3062 | semidirect |
| 156. #535 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813648 | 2 |
| C2×#16813629 | 2 |
| #20299176 | 2 |
| #20298849 | 2 |
| #20298842 | 2 |
| #20298832 | 2 |
| #20298825 | 2 |
| #20298641 | 2 |
| #20298592 | 2 |
| C2×#16813543 | 2 |
| #535×C113 | 2 |
| #3062 | 113 |