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×#16813630 | C2 | semidirect |
| 3. #20299179 | C2 | semidirect |
| 4. #20299167 | C2 | semidirect |
| 5. #20298852 | C2 | semidirect |
| 6. #20298845 | C2 | semidirect |
| 7. #20298835 | C2 | semidirect |
| 8. #20298828 | C2 | semidirect |
| 9. #20298592 | C2 | semidirect |
| 10. C2×#16813542 | C2 | semidirect |
| 11. #428×C113 | C2 | semidirect |
| 19. C2×#14268630 | C22 | semidirect |
| 21. C2×C8×D113 | C22 | semidirect |
| 25. #16813602 | C22 | semidirect |
| 29. #16813597 | C22 | semidirect |
| 32. #16813545 | C22 | semidirect |
| 33. #16813545 | C22 | semidirect |
| 36. #16813542 | C22 | semidirect |
| 37. #16813542 | C22 | semidirect |
| 41. #107×C113 | C22 | semidirect |
| 42. #106×C113 | C22 | semidirect |
| 77. M16×C113 | D4 | semidirect |
| 152. C113 | #3062 | semidirect |
| 161. #428 | D113 | semidirect |
| 187. #107 | C2×D113 | semidirect |
| 188. #106 | C2×D113 | semidirect |
| 220. M16 | D452 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813650 | 2 |
| C2×#16813630 | 2 |
| #20299179 | 2 |
| #20299167 | 2 |
| #20298852 | 2 |
| #20298845 | 2 |
| #20298835 | 2 |
| #20298828 | 2 |
| #20298592 | 2 |
| C2×#16813542 | 2 |
| #428×C113 | 2 |
| #3062 | 113 |