Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
1412 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1412 conjugacy classes of subgroups — too many to draw. Only its 545 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×#16813669 | C2 | semidirect |
| 2. #20299413 | C2 | semidirect |
| 3. #20299409 | C2 | semidirect |
| 4. #20299396 | C2 | semidirect |
| 5. C2×#16813652 | C2 | semidirect |
| 6. #20299365 | C2 | semidirect |
| 7. #585×C113 | C2 | semidirect |
| 9. #16813669 | C22 | semidirect |
| 10. C2×#14268647 | C22 | semidirect |
| 12. C22×Dic226 | C22 | semidirect |
| 14. #16813653 | C22 | semidirect |
| 15. #16813652 | C22 | semidirect |
| 16. #16813652 | C22 | semidirect |
| 17. #16813648 | C22 | semidirect |
| 18. #16813647 | C22 | semidirect |
| 19. #16813642 | C22 | semidirect |
| 20. C2×#14268637 | C22 | semidirect |
| 21. C2×#14268635 | C22 | semidirect |
| 22. #16813629 | C22 | semidirect |
| 23. C2×#14268631 | C22 | semidirect |
| 25. 2−1+4×C113 | C22 | semidirect |
| 27. H(5,𝔽2)×C113 | C22 | semidirect |
| 113. C113 | #3586 | semidirect |
| 114. #585 | D113 | semidirect |
| 124. 2−1+4 | C2×D113 | semidirect |
| 126. H(5,𝔽2) | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813669 | 2 |
| #20299413 | 2 |
| #20299409 | 2 |
| #20299396 | 2 |
| C2×#16813652 | 2 |
| #20299365 | 2 |
| #585×C113 | 2 |
| #3586 | 113 |