Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#16813650 | C2 | semidirect |
| 2. C2×#16813642 | C2 | semidirect |
| 3. #20299162 | C2 | semidirect |
| 4. #20299079 | C2 | semidirect |
| 5. #20298823 | C2 | semidirect |
| 6. #20298816 | C2 | semidirect |
| 7. #20298797 | C2 | semidirect |
| 8. #20298792 | C2 | semidirect |
| 9. #20298626 | C2 | semidirect |
| 10. C2×#16813542 | C2 | semidirect |
| 11. #417×C113 | C2 | semidirect |
| 16. C2×#14268637 | C22 | semidirect |
| 18. C2×#14268635 | C22 | semidirect |
| 19. C2×#14268634 | C22 | semidirect |
| 21. C2×#14268632 | C22 | semidirect |
| 28. #16813587 | C22 | semidirect |
| 29. #16813584 | C22 | semidirect |
| 34. #16813551 | C22 | semidirect |
| 35. #16813551 | C22 | semidirect |
| 41. #103×C113 | C22 | semidirect |
| 42. #102×C113 | C22 | semidirect |
| 45. #14268647 | D4 | semidirect |
| 155. C113 | #3045 | semidirect |
| 165. #417 | D113 | semidirect |
| 194. #103 | C2×D113 | semidirect |
| 197. #102 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813650 | 2 |
| C2×#16813642 | 2 |
| #20299162 | 2 |
| #20299079 | 2 |
| #20298823 | 2 |
| #20298816 | 2 |
| #20298797 | 2 |
| #20298792 | 2 |
| #20298626 | 2 |
| C2×#16813542 | 2 |
| #417×C113 | 2 |
| #3045 | 113 |