Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20299210 | C2 | semidirect |
| 2. #20298993 | C2 | semidirect |
| 3. #20298970 | C2 | semidirect |
| 4. #20298962 | C2 | semidirect |
| 5. #20298952 | C2 | semidirect |
| 6. #20298817 | C2 | semidirect |
| 7. #20298795 | C2 | semidirect |
| 8. #20298760 | C2 | semidirect |
| 9. #20298749 | C2 | semidirect |
| 10. #20298659 | C2 | semidirect |
| 12. C2×#14268637 | C22 | semidirect |
| 15. C2×#14268635 | C22 | semidirect |
| 16. #16813622 | C22 | semidirect |
| 18. #16813614 | C22 | semidirect |
| 21. C4×Dic226 | C22 | semidirect |
| 22. C4⋊#11744751 | C22 | semidirect |
| 23. #16813546 | C22 | semidirect |
| 26. #16813543 | C22 | semidirect |
| 28. #16813533 | C22 | semidirect |
| 29. C4×#11744751 | C22 | semidirect |
| 123. C113 | #3222 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299210 | 2 |
| #20298993 | 2 |
| #20298970 | 2 |
| #20298962 | 2 |
| #20298952 | 2 |
| #20298817 | 2 |
| #20298795 | 2 |
| #20298760 | 2 |
| #20298749 | 2 |
| #20298659 | 2 |
| #535×C113 | 2 |
| #3222 | 113 |