Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20299229 | C2 | semidirect |
| 3. #20298961 | C2 | semidirect |
| 4. #20298956 | C2 | semidirect |
| 5. #20298951 | C2 | semidirect |
| 6. #20298943 | C2 | semidirect |
| 7. #20298603 | C2 | semidirect |
| 8. #20298597 | C2 | semidirect |
| 9. #20298595 | C2 | semidirect |
| 10. #20298553 | C2 | semidirect |
| 11. C2×#102×C113 | C2 | semidirect |
| 15. #16813621 | C22 | semidirect |
| 18. #16813613 | C22 | semidirect |
| 26. #16813547 | C22 | semidirect |
| 27. #16813547 | C22 | semidirect |
| 28. #16813545 | C22 | semidirect |
| 29. #16813544 | C22 | semidirect |
| 30. #16813544 | C22 | semidirect |
| 33. #16813542 | C22 | semidirect |
| 34. #16813532 | C22 | semidirect |
| 35. C8×Dic113 | C22 | semidirect |
| 136. C113 | #3136 | semidirect |
| 146. C2×#102 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299229 | 2 |
| #20299165 | 2 |
| #20298961 | 2 |
| #20298956 | 2 |
| #20298951 | 2 |
| #20298943 | 2 |
| #20298603 | 2 |
| #20298597 | 2 |
| #20298595 | 2 |
| #20298553 | 2 |
| C2×#102×C113 | 2 |
| #3136 | 113 |