Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 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. #20299396 | C2 | semidirect |
| 2. C2×#16813648 | C2 | semidirect |
| 3. #20299364 | C2 | semidirect |
| 4. #20298865 | C2 | semidirect |
| 5. #20298858 | C2 | semidirect |
| 6. #20298647 | C2 | semidirect |
| 7. #20298582 | C2 | semidirect |
| 8. C2×#16813539 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C113 | C2 | semidirect |
| 11. #16813653 | C22 | semidirect |
| 15. #16813648 | C22 | semidirect |
| 21. #16813628 | C22 | semidirect |
| 26. #16813558 | C22 | semidirect |
| 27. #16813541 | C22 | semidirect |
| 28. #16813539 | C22 | semidirect |
| 29. #16813539 | C22 | semidirect |
| 34. C2×SD16×C113 | C22 | semidirect |
| 35. C2×D8×C113 | C22 | semidirect |
| 148. C113 | #3068 | semidirect |
| 151. C2×AGL(1,ℤ/8) | D113 | semidirect |
| 171. C2×SD16 | C2×D113 | semidirect |
| 173. C2×D8 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299396 | 2 |
| C2×#16813648 | 2 |
| #20299364 | 2 |
| #20298865 | 2 |
| #20298858 | 2 |
| #20298647 | 2 |
| #20298582 | 2 |
| C2×#16813539 | 2 |
| C2×AGL(1,ℤ/8)×C113 | 2 |
| #3068 | 113 |