Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
532 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 532 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×#16813618 | C2 | semidirect |
| 3. #20298973 | C2 | semidirect |
| 4. #20298943 | C2 | semidirect |
| 5. #20298792 | C2 | semidirect |
| 6. #20298791 | C2 | semidirect |
| 7. #20298734 | C2 | semidirect |
| 8. #20298732 | C2 | semidirect |
| 9. #20298731 | C2 | semidirect |
| 10. #20298648 | C2 | semidirect |
| 11. #447×C113 | C2 | semidirect |
| 16. C2×D904 | C22 | semidirect |
| 17. C2×#14268632 | C22 | semidirect |
| 18. C2×#14268632 | C22 | semidirect |
| 19. #16813621 | C22 | semidirect |
| 24. #16813618 | C22 | semidirect |
| 28. D4×Dic113 | C22 | semidirect |
| 29. #16813584 | C22 | semidirect |
| 32. #16813551 | C22 | semidirect |
| 33. #16813544 | C22 | semidirect |
| 34. #16813543 | C22 | semidirect |
| 35. #16813542 | C22 | semidirect |
| 37. C8×Dic113 | C22 | semidirect |
| 39. C2×D8×C113 | C22 | semidirect |
| 41. #102×C113 | C22 | semidirect |
| 117. C2×Dic113 | D8 | semidirect |
| 165. C113 | #3205 | semidirect |
| 175. #447 | D113 | semidirect |
| 185. C2×D8 | C2×D113 | semidirect |
| 204. #102 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299143 | 2 |
| C2×#16813618 | 2 |
| #20298973 | 2 |
| #20298943 | 2 |
| #20298792 | 2 |
| #20298791 | 2 |
| #20298734 | 2 |
| #20298732 | 2 |
| #20298731 | 2 |
| #20298648 | 2 |
| #447×C113 | 2 |
| #3205 | 113 |