Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16813655 | C2 | semidirect |
| 3. C2×#16813610 | C2 | semidirect |
| 4. C4×#14268647 | C2 | semidirect |
| 5. #20298821 | C2 | semidirect |
| 6. #20298814 | C2 | semidirect |
| 7. #20298608 | C2 | semidirect |
| 8. #20298604 | C2 | semidirect |
| 9. #423×C113 | C2 | semidirect |
| 15. C2×Dic452 | C22 | semidirect |
| 17. C2×#14268636 | C22 | semidirect |
| 22. C4×Dic226 | C22 | semidirect |
| 23. C4×D452 | C22 | semidirect |
| 29. #16813547 | C22 | semidirect |
| 34. C4⋊C8×C113 | C22 | semidirect |
| 126. C113 | #3040 | semidirect |
| 133. #423 | D113 | semidirect |
| 158. C4⋊C8 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813655 | 2 |
| C2×#16813650 | 2 |
| C2×#16813610 | 2 |
| C4×#14268647 | 2 |
| #20298821 | 2 |
| #20298814 | 2 |
| #20298608 | 2 |
| #20298604 | 2 |
| #423×C113 | 2 |
| #3040 | 113 |