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×#16813647 | C2 | semidirect |
| 2. C2×#16813629 | C2 | semidirect |
| 3. #20299162 | C2 | semidirect |
| 4. #20298849 | C2 | semidirect |
| 5. #20298846 | C2 | semidirect |
| 6. #20298832 | C2 | semidirect |
| 7. #20298829 | C2 | semidirect |
| 8. #20298638 | C2 | semidirect |
| 9. #20298594 | C2 | semidirect |
| 10. C2×#16813542 | C2 | semidirect |
| 11. #537×C113 | C2 | semidirect |
| 18. C2×#14268631 | C22 | semidirect |
| 20. C22×#11744751 | C22 | semidirect |
| 27. #16813555 | C22 | semidirect |
| 28. #16813553 | C22 | semidirect |
| 29. #16813546 | C22 | semidirect |
| 30. #16813546 | C22 | semidirect |
| 31. #16813543 | C22 | semidirect |
| 32. #16813543 | C22 | semidirect |
| 38. C22⋊Q8×C113 | C22 | semidirect |
| 41. #121×C113 | C22 | semidirect |
| 53. #14268631 | D4 | semidirect |
| 152. C113 | #3062 | semidirect |
| 155. #537 | D113 | semidirect |
| 178. C22⋊Q8 | C2×D113 | semidirect |
| 183. #121 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813647 | 2 |
| C2×#16813629 | 2 |
| #20299162 | 2 |
| #20298849 | 2 |
| #20298846 | 2 |
| #20298832 | 2 |
| #20298829 | 2 |
| #20298638 | 2 |
| #20298594 | 2 |
| C2×#16813542 | 2 |
| #537×C113 | 2 |
| #3062 | 113 |