Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
532 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20299149 | C2 | semidirect |
| 2. #127×D113 | C2 | semidirect |
| 3. #20298975 | C2 | semidirect |
| 4. #20298974 | C2 | semidirect |
| 5. #20298946 | C2 | semidirect |
| 6. #20298792 | C2 | semidirect |
| 7. #20298733 | C2 | semidirect |
| 8. #20298649 | C2 | semidirect |
| 9. #486×C113 | C2 | semidirect |
| 14. C2×D904 | C22 | semidirect |
| 15. C2×#14268632 | C22 | semidirect |
| 17. #16813619 | C22 | semidirect |
| 25. #16813584 | C22 | semidirect |
| 27. #16813551 | C22 | semidirect |
| 28. #16813542 | C22 | semidirect |
| 30. C4×#11744751 | C22 | semidirect |
| 31. C4⋊Q8×C113 | C22 | semidirect |
| 33. #102×C113 | C22 | semidirect |
| 34. C4×C8×C113 | C22 | semidirect |
| 101. C4×D113 | D8 | semidirect |
| 133. C113 | #3205 | semidirect |
| 139. #486 | D113 | semidirect |
| 149. C4⋊Q8 | C2×D113 | semidirect |
| 164. #102 | C2×D113 | semidirect |
| 167. C4×C8 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299149 | 2 |
| #127×D113 | 2 |
| #20298975 | 2 |
| #20298974 | 2 |
| #20298946 | 2 |
| #20298792 | 2 |
| #20298733 | 2 |
| #20298649 | 2 |
| #486×C113 | 2 |
| #3205 | 113 |