Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
370 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 129 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. #20299403 | C2 | semidirect |
| 2. #20299036 | C2 | semidirect |
| 3. #20299030 | C2 | semidirect |
| 4. C2×D1808 | C2 | semidirect |
| 5. #504×C113 | C2 | semidirect |
| 8. #16813644 | C22 | semidirect |
| 9. C2×D904 | C22 | semidirect |
| 10. Dic904 | C22 | semidirect |
| 11. #16813567 | C22 | semidirect |
| 12. D1808 | C22 | semidirect |
| 13. D1808 | C22 | semidirect |
| 15. M32×C113 | C22 | semidirect |
| 16. C2×C16×C113 | C22 | semidirect |
| 51. C113 | #3415 | semidirect |
| 56. #504 | D113 | semidirect |
| 66. M32 | C2×D113 | semidirect |
| 67. C2×C16 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299403 | 2 |
| #20299036 | 2 |
| #20299030 | 2 |
| C2×D1808 | 2 |
| #504×C113 | 2 |
| #3415 | 113 |