Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
488 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 129 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. #20299148 | C2 | semidirect |
| 2. C2×C4×D452 | C2 | semidirect |
| 3. #20298917 | C2 | semidirect |
| 4. #20298889 | C2 | semidirect |
| 5. #20298794 | C2 | semidirect |
| 6. #20298734 | C2 | semidirect |
| 7. #20298711 | C2 | semidirect |
| 8. #432×C113 | C2 | semidirect |
| 13. #16813622 | C22 | semidirect |
| 14. #16813619 | C22 | semidirect |
| 23. C4×D452 | C22 | semidirect |
| 26. #16813554 | C22 | semidirect |
| 28. #16813544 | C22 | semidirect |
| 30. C4⋊C8×C113 | C22 | semidirect |
| 32. #97×C113 | C22 | semidirect |
| 89. D452 | #41 | semidirect |
| 121. C113 | #3109 | semidirect |
| 129. #432 | D113 | semidirect |
| 149. C4⋊C8 | C2×D113 | semidirect |
| 153. #97 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299148 | 2 |
| C2×C4×D452 | 2 |
| #20298917 | 2 |
| #20298889 | 2 |
| #20298794 | 2 |
| #20298734 | 2 |
| #20298711 | 2 |
| #432×C113 | 2 |
| #3109 | 113 |