Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
488 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20299143 | C2 | semidirect |
| 2. C2×D4×Dic113 | C2 | semidirect |
| 3. #20298917 | C2 | semidirect |
| 4. #20298914 | C2 | semidirect |
| 5. #20298886 | C2 | semidirect |
| 6. #20298791 | C2 | semidirect |
| 7. #20298732 | C2 | semidirect |
| 8. #20298710 | C2 | semidirect |
| 9. #20298707 | C2 | semidirect |
| 10. #20298652 | C2 | semidirect |
| 11. #447×C113 | C2 | semidirect |
| 15. #16813621 | C22 | semidirect |
| 16. #16813618 | C22 | semidirect |
| 24. D4×Dic113 | C22 | semidirect |
| 25. #16813584 | C22 | semidirect |
| 30. #16813554 | C22 | semidirect |
| 31. #16813553 | C22 | semidirect |
| 32. #16813551 | C22 | semidirect |
| 33. #16813544 | C22 | semidirect |
| 35. #16813543 | C22 | semidirect |
| 37. #16813532 | C22 | semidirect |
| 94. D4×C113 | #41 | semidirect |
| 150. C113 | #3109 | semidirect |
| 158. #447 | D113 | semidirect |
| 249. D4 | #14268646 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299143 | 2 |
| C2×D4×Dic113 | 2 |
| #20298917 | 2 |
| #20298914 | 2 |
| #20298886 | 2 |
| #20298791 | 2 |
| #20298732 | 2 |
| #20298710 | 2 |
| #20298707 | 2 |
| #20298652 | 2 |
| #447×C113 | 2 |
| #3109 | 113 |