Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×#14268635 | C2 | semidirect |
| 2. C22×#14268631 | C2 | semidirect |
| 3. C2×#16813601 | C2 | semidirect |
| 4. #20298842 | C2 | direct (N × H) |
| 5. C2×#16813555 | C2 | semidirect |
| 6. C2×#16813545 | C2 | semidirect |
| 7. C2×#16813543 | C2 | semidirect |
| 11. C2×#14268635 | C22 | semidirect |
| 13. C2×#14268631 | C22 | semidirect |
| 17. #16813601 | C22 | semidirect |
| 21. #16813555 | C22 | semidirect |
| 22. #16813545 | C22 | semidirect |
| 23. #16813543 | C22 | semidirect |
| 40. C2×#11744751 | D4 | semidirect |
| 97. #11744751 | C2×D4 | semidirect |
| 119. C2×C113 | #468 | semidirect |
| 124. C113 | C2×#468 | semidirect |
| 243. C2 | #20298842 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14268635 | 2 |
| C22×#14268631 | 2 |
| C2×#16813601 | 2 |
| #20298842 | 2 |
| C2×#16813555 | 2 |
| C2×#16813545 | 2 |
| C2×#16813543 | 2 |
| C2×#121×C113 | 2 |
| C2×#468 | 113 |