Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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×#16813647 | C2 | semidirect |
| 2. C2×#16813647 | C2 | semidirect |
| 3. #20299365 | C2 | semidirect |
| 4. #20298866 | C2 | semidirect |
| 5. #20298863 | C2 | semidirect |
| 6. #20298646 | C2 | semidirect |
| 7. #20298582 | C2 | semidirect |
| 8. C2×#16813538 | C2 | semidirect |
| 9. #575×C113 | C2 | semidirect |
| 16. C2×#14268634 | C22 | semidirect |
| 18. C2×#14268632 | C22 | semidirect |
| 20. #16813629 | C22 | semidirect |
| 25. #16813557 | C22 | semidirect |
| 26. #16813541 | C22 | semidirect |
| 27. #16813539 | C22 | semidirect |
| 28. #16813538 | C22 | semidirect |
| 32. #137×C113 | C22 | semidirect |
| 34. AGL(1,ℤ/8)×C113 | C22 | semidirect |
| 148. C113 | #3068 | semidirect |
| 149. #575 | D113 | semidirect |
| 162. #137 | C2×D113 | semidirect |
| 168. AGL(1,ℤ/8) | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813647 | 2 |
| #20299365 | 2 |
| #20298866 | 2 |
| #20298863 | 2 |
| #20298646 | 2 |
| #20298582 | 2 |
| C2×#16813538 | 2 |
| #575×C113 | 2 |
| #3068 | 113 |