Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 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. #20299226 | C2 | semidirect |
| 2. #20298962 | C2 | semidirect |
| 3. #20298957 | C2 | semidirect |
| 4. #20298952 | C2 | semidirect |
| 5. #20298944 | C2 | semidirect |
| 6. #20298603 | C2 | semidirect |
| 7. #20298599 | C2 | semidirect |
| 8. #20298594 | C2 | semidirect |
| 9. C2×#16813543 | C2 | semidirect |
| 10. #20298554 | C2 | semidirect |
| 14. #16813622 | C22 | semidirect |
| 16. #16813614 | C22 | semidirect |
| 21. #16813546 | C22 | semidirect |
| 22. #16813546 | C22 | semidirect |
| 23. #16813546 | C22 | semidirect |
| 28. #16813543 | C22 | semidirect |
| 29. #16813543 | C22 | semidirect |
| 30. #16813543 | C22 | semidirect |
| 31. #16813533 | C22 | semidirect |
| 32. C4×#11744751 | C22 | semidirect |
| 136. C113 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299226 | 2 |
| #20298962 | 2 |
| #20298957 | 2 |
| #20298952 | 2 |
| #20298944 | 2 |
| #20298603 | 2 |
| #20298599 | 2 |
| #20298594 | 2 |
| C2×#16813543 | 2 |
| #20298554 | 2 |
| #535×C113 | 2 |
| #3136 | 113 |