Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
456 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 217 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×#16813629 | C2 | semidirect |
| 2. #20298720 | C2 | semidirect |
| 3. #20298715 | C2 | semidirect |
| 4. #20298647 | C2 | semidirect |
| 5. #20298615 | C2 | semidirect |
| 6. #20298556 | C2 | semidirect |
| 10. #16813629 | C22 | semidirect |
| 11. #16813629 | C22 | semidirect |
| 17. #16813558 | C22 | semidirect |
| 18. #16813549 | C22 | semidirect |
| 19. #16813532 | C22 | semidirect |
| 20. C8×Dic113 | C22 | semidirect |
| 22. #137×C113 | C4 | semidirect |
| 23. AGL(1,ℤ/8)×C113 | C4 | semidirect |
| 90. C113 | #2955 | semidirect |
| 99. #137 | Dic113 | semidirect |
| 100. AGL(1,ℤ/8) | Dic113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813629 | 2 |
| #20298720 | 2 |
| #20298715 | 2 |
| #20298647 | 2 |
| #20298615 | 2 |
| #20298556 | 2 |
| #575×C113 | 2 |
| #2955 | 113 |