Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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. #20299132 | C2 | semidirect |
| 2. C2×#16813610 | C2 | semidirect |
| 3. #20298982 | C2 | semidirect |
| 4. #20298953 | C2 | semidirect |
| 5. #20298821 | C2 | semidirect |
| 6. #20298814 | C2 | semidirect |
| 7. #20298756 | C2 | semidirect |
| 8. #20298751 | C2 | semidirect |
| 9. #20298739 | C2 | semidirect |
| 11. #431×C113 | C2 | semidirect |
| 14. C2×Dic452 | C22 | semidirect |
| 16. C2×#14268636 | C22 | semidirect |
| 19. #16813614 | C22 | semidirect |
| 24. #16813610 | C22 | semidirect |
| 28. C4×Dic226 | C22 | semidirect |
| 29. C4×D452 | C22 | semidirect |
| 34. #16813547 | C22 | semidirect |
| 35. #16813547 | C22 | semidirect |
| 39. C4⋊C8×C113 | C22 | semidirect |
| 42. C4×C8×C113 | C22 | semidirect |
| 144. C113 | #3211 | semidirect |
| 155. #431 | D113 | semidirect |
| 179. C4⋊C8 | C2×D113 | semidirect |
| 186. C4×C8 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299132 | 2 |
| C2×#16813610 | 2 |
| #20298982 | 2 |
| #20298953 | 2 |
| #20298821 | 2 |
| #20298814 | 2 |
| #20298756 | 2 |
| #20298751 | 2 |
| #20298739 | 2 |
| #20298734 | 2 |
| #431×C113 | 2 |
| #3211 | 113 |