Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
490 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 490 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. C2×#16813619 | C2 | semidirect |
| 2. #20298988 | C2 | semidirect |
| 3. #20298964 | C2 | semidirect |
| 4. #20298798 | C2 | semidirect |
| 5. #20298793 | C2 | semidirect |
| 6. #20298748 | C2 | semidirect |
| 7. #20298731 | C2 | semidirect |
| 8. #20298655 | C2 | semidirect |
| 9. #529×C113 | C2 | semidirect |
| 13. C2×#14268634 | C22 | semidirect |
| 14. C2×#14268632 | C22 | semidirect |
| 19. C4⋊#11744751 | C22 | semidirect |
| 20. #16813542 | C22 | semidirect |
| 21. #16813542 | C22 | semidirect |
| 23. #16813533 | C22 | semidirect |
| 25. #125×C113 | C22 | semidirect |
| 26. #124×C113 | C22 | semidirect |
| 30. C4×Q8×C113 | C22 | semidirect |
| 32. C4×D4×C113 | C22 | semidirect |
| 128. C113 | #3217 | semidirect |
| 130. #529 | D113 | semidirect |
| 148. #125 | C2×D113 | semidirect |
| 149. #124 | C2×D113 | semidirect |
| 153. C4×Q8 | C2×D113 | semidirect |
| 155. C4×D4 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813619 | 2 |
| #20298988 | 2 |
| #20298964 | 2 |
| #20298798 | 2 |
| #20298793 | 2 |
| #20298748 | 2 |
| #20298731 | 2 |
| #20298655 | 2 |
| #529×C113 | 2 |
| #3217 | 113 |