Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
468 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#16813601 | C2 | semidirect |
| 3. #20298929 | C2 | semidirect |
| 4. #20298917 | C2 | semidirect |
| 5. #20298827 | C2 | semidirect |
| 6. #20298751 | C2 | semidirect |
| 7. #20298739 | C2 | semidirect |
| 8. C2×C22⋊C8×C113 | C2 | semidirect |
| 9. C22×Dic226 | C22 | semidirect |
| 12. C2×#14268636 | C22 | semidirect |
| 16. #16813601 | C22 | semidirect |
| 22. C2×C4⋊Dic113 | C22 | semidirect |
| 26. #16813554 | C22 | semidirect |
| 27. #16813547 | C22 | semidirect |
| 28. #16813544 | C22 | semidirect |
| 30. C22×C8×C113 | C22 | semidirect |
| 32. C22⋊C8×C113 | C22 | semidirect |
| 69. C23×C113 | SD16 | semidirect |
| 130. C113 | #3187 | semidirect |
| 138. C2×C22⋊C8 | D113 | semidirect |
| 144. C22×C8 | C2×D113 | semidirect |
| 162. C22⋊C8 | C2×D113 | semidirect |
| 203. C23 | #14268636 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813601 | 2 |
| C2×#16813596 | 2 |
| #20298929 | 2 |
| #20298917 | 2 |
| #20298827 | 2 |
| #20298751 | 2 |
| #20298739 | 2 |
| C2×C22⋊C8×C113 | 2 |
| #3187 | 113 |