Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 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×#16813647 | C2 | semidirect |
| 2. C22×#14268632 | C2 | semidirect |
| 3. C2×#16813629 | C2 | semidirect |
| 4. #20298866 | C2 | direct (N × H) |
| 5. C2×#16813557 | C2 | semidirect |
| 6. C2×#16813539 | C2 | semidirect |
| 7. C2×#16813538 | C2 | semidirect |
| 8. C2×AGL(1,ℤ/8)×C113 | C2 | semidirect |
| 11. #16813647 | C22 | semidirect |
| 17. C2×#14268632 | C22 | semidirect |
| 19. #16813629 | C22 | semidirect |
| 25. #16813557 | C22 | semidirect |
| 26. #16813539 | C22 | semidirect |
| 27. #16813538 | C22 | semidirect |
| 31. AGL(1,ℤ/8)×C113 | C22 | semidirect |
| 140. C2×C113 | #472 | semidirect |
| 144. C113 | C2×#472 | semidirect |
| 146. C2×AGL(1,ℤ/8) | D113 | semidirect |
| 159. AGL(1,ℤ/8) | C2×D113 | semidirect |
| 285. C2 | #20298866 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813647 | 2 |
| C22×#14268632 | 2 |
| C2×#16813629 | 2 |
| #20298866 | 2 |
| C2×#16813557 | 2 |
| C2×#16813539 | 2 |
| C2×#16813538 | 2 |
| C2×AGL(1,ℤ/8)×C113 | 2 |
| C2×#472 | 113 |