Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
462 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 139 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. #20299305 | C2 | semidirect |
| 3. #20298945 | C2 | semidirect |
| 4. #20298917 | C2 | semidirect |
| 5. #20298889 | C2 | semidirect |
| 6. #20298827 | C2 | semidirect |
| 7. #20298799 | C2 | semidirect |
| 8. #20298751 | C2 | semidirect |
| 9. C4×#14268636 | C2 | semidirect |
| 10. C2×#16813544 | C2 | semidirect |
| 11. C8×D4×C113 | C2 | semidirect |
| 15. C2×#14268636 | C22 | semidirect |
| 16. #16813622 | C22 | semidirect |
| 19. #16813601 | C22 | semidirect |
| 24. C4×Dic226 | C22 | semidirect |
| 27. C2×C4⋊Dic113 | C22 | semidirect |
| 28. #16813554 | C22 | semidirect |
| 29. #16813554 | C22 | semidirect |
| 30. #16813547 | C22 | semidirect |
| 33. #16813544 | C22 | semidirect |
| 34. #16813544 | C22 | semidirect |
| 35. #16813544 | C22 | semidirect |
| 36. C22×C8×C113 | C22 | semidirect |
| 38. C4⋊C8×C113 | C22 | semidirect |
| 39. C22⋊C8×C113 | C22 | semidirect |
| 40. C4×C8×C113 | C22 | semidirect |
| 83. D4×C113 | SD16 | semidirect |
| 137. C113 | #3295 | semidirect |
| 147. C8×D4 | D113 | semidirect |
| 153. C22×C8 | C2×D113 | semidirect |
| 169. C4⋊C8 | C2×D113 | semidirect |
| 176. C22⋊C8 | C2×D113 | semidirect |
| 177. C4×C8 | C2×D113 | semidirect |
| 231. D4 | #14268636 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299305 | 2 |
| D4×D452 | 2 |
| #20298945 | 2 |
| #20298917 | 2 |
| #20298889 | 2 |
| #20298827 | 2 |
| #20298799 | 2 |
| #20298751 | 2 |
| C4×#14268636 | 2 |
| C2×#16813544 | 2 |
| C8×D4×C113 | 2 |
| #3295 | 113 |