Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
492 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 127 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. #20299146 | C2 | semidirect |
| 2. C4×D4×D113 | C2 | semidirect |
| 3. #20298910 | C2 | semidirect |
| 4. #20298879 | C2 | semidirect |
| 5. #20298878 | C2 | semidirect |
| 6. #20298790 | C2 | semidirect |
| 7. #20298730 | C2 | semidirect |
| 8. D8×Dic113 | C2 | semidirect |
| 9. #20298678 | C2 | semidirect |
| 10. #20298650 | C2 | semidirect |
| 11. #459×C113 | C2 | semidirect |
| 16. #16813622 | C22 | semidirect |
| 23. D4×Dic113 | C22 | semidirect |
| 30. #16813556 | C22 | semidirect |
| 31. #16813555 | C22 | semidirect |
| 32. C4⋊#11744751 | C22 | semidirect |
| 35. #16813543 | C22 | semidirect |
| 37. C8×Dic113 | C22 | semidirect |
| 39. #127×C113 | C22 | semidirect |
| 41. C4⋊C8×C113 | C22 | semidirect |
| 42. #102×C113 | C22 | semidirect |
| 96. D4×C113 | #41 | semidirect |
| 112. D452 | #41 | semidirect |
| 119. C4×D113 | D8 | semidirect |
| 155. C113 | #3100 | semidirect |
| 162. #459 | D113 | semidirect |
| 173. #127 | C2×D113 | semidirect |
| 191. C4⋊C8 | C2×D113 | semidirect |
| 195. #102 | C2×D113 | semidirect |
| 256. D4 | #14268646 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299146 | 2 |
| C4×D4×D113 | 2 |
| #20298910 | 2 |
| #20298879 | 2 |
| #20298878 | 2 |
| #20298790 | 2 |
| #20298730 | 2 |
| D8×Dic113 | 2 |
| #20298678 | 2 |
| #20298650 | 2 |
| #459×C113 | 2 |
| #3100 | 113 |