Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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×#16813668 | C2 | semidirect |
| 2. C2×#16813647 | C2 | semidirect |
| 3. C22×D904 | C2 | semidirect |
| 4. #20299167 | C2 | semidirect |
| 5. #20298746 | C2 | semidirect |
| 6. #20298733 | C2 | semidirect |
| 7. #20298602 | C2 | semidirect |
| 8. #20298564 | C2 | semidirect |
| 9. #416×C113 | C2 | semidirect |
| 12. C2×#14268648 | C22 | semidirect |
| 17. C22×D452 | C22 | semidirect |
| 19. C2×D4×D113 | C22 | semidirect |
| 21. C2×#14268634 | C22 | semidirect |
| 23. C2×D904 | C22 | semidirect |
| 24. C2×#14268632 | C22 | semidirect |
| 25. C2×#14268631 | C22 | semidirect |
| 28. #16813597 | C22 | semidirect |
| 30. #16813542 | C22 | semidirect |
| 31. #16813534 | C22 | semidirect |
| 33. C22×C8×C113 | C22 | semidirect |
| 34. #117×C113 | C22 | semidirect |
| 35. #103×C113 | C22 | semidirect |
| 36. #102×C113 | C22 | semidirect |
| 55. C2×D452 | D4 | semidirect |
| 72. #41×C113 | D4 | semidirect |
| 152. C113 | #3008 | semidirect |
| 160. #416 | D113 | semidirect |
| 179. C22×C8 | C2×D113 | semidirect |
| 184. #117 | C2×D113 | semidirect |
| 185. #103 | C2×D113 | semidirect |
| 187. #102 | C2×D113 | semidirect |
| 198. #41 | D452 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813668 | 2 |
| C2×#16813647 | 2 |
| C22×D904 | 2 |
| #20299167 | 2 |
| #20298746 | 2 |
| #20298733 | 2 |
| #20298602 | 2 |
| #20298564 | 2 |
| #416×C113 | 2 |
| #3008 | 113 |