Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16813650 | C2 | semidirect |
| 2. C2×#16813644 | C2 | semidirect |
| 3. #20299167 | C2 | semidirect |
| 4. #20299078 | C2 | semidirect |
| 5. #20298821 | C2 | semidirect |
| 6. #20298814 | C2 | semidirect |
| 7. #20298799 | C2 | semidirect |
| 8. #20298794 | C2 | semidirect |
| 9. #20298600 | C2 | semidirect |
| 10. C2×#16813544 | C2 | semidirect |
| 11. #424×C113 | C2 | semidirect |
| 17. C2×Dic452 | C22 | semidirect |
| 19. C2×#14268636 | C22 | semidirect |
| 20. C2×#14268636 | C22 | semidirect |
| 22. C2×D904 | C22 | semidirect |
| 28. C4×Dic226 | C22 | semidirect |
| 29. C4×D452 | C22 | semidirect |
| 34. #16813547 | C22 | semidirect |
| 37. #16813544 | C22 | semidirect |
| 41. C4⋊C8×C113 | C22 | semidirect |
| 42. C4⋊C8×C113 | C22 | semidirect |
| 47. #14268647 | D4 | semidirect |
| 155. C113 | #3045 | semidirect |
| 164. #424 | D113 | semidirect |
| 192. C4⋊C8 | C2×D113 | semidirect |
| 193. C4⋊C8 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813650 | 2 |
| C2×#16813644 | 2 |
| #20299167 | 2 |
| #20299078 | 2 |
| #20298821 | 2 |
| #20298814 | 2 |
| #20298799 | 2 |
| #20298794 | 2 |
| #20298600 | 2 |
| C2×#16813544 | 2 |
| #424×C113 | 2 |
| #3045 | 113 |