Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
548 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 2. #20298616 | C2 | semidirect |
| 3. #20298615 | C2 | semidirect |
| 4. #20298595 | C2 | semidirect |
| 5. #20298571 | C2 | semidirect |
| 6. #20298564 | C2 | semidirect |
| 7. #416×C113 | C2 | semidirect |
| 10. #16813669 | C4 | semidirect |
| 12. #16813668 | C4 | semidirect |
| 20. C2×#14268631 | C22 | semidirect |
| 21. #16813581 | C22 | semidirect |
| 29. C22×C8×C113 | C22 | semidirect |
| 30. #117×C113 | C22 | semidirect |
| 167. C113 | #1794 | semidirect |
| 172. #416 | D113 | semidirect |
| 189. C22×C8 | C2×D113 | semidirect |
| 191. #117 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299434 | 2 |
| #20298616 | 2 |
| #20298615 | 2 |
| #20298595 | 2 |
| #20298571 | 2 |
| #20298564 | 2 |
| #416×C113 | 2 |
| #1794 | 113 |