Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
472 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 125 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×#16813596 | C2 | semidirect |
| 2. #20298931 | C2 | semidirect |
| 3. #20298922 | C2 | semidirect |
| 4. #20298914 | C2 | semidirect |
| 5. #20298832 | C2 | semidirect |
| 6. #20298829 | C2 | semidirect |
| 7. #20298748 | C2 | semidirect |
| 8. #20298743 | C2 | semidirect |
| 9. #20298731 | C2 | semidirect |
| 10. C2×C22⋊#11744751 | C2 | semidirect |
| 11. #525×C113 | C2 | semidirect |
| 14. C2×#14268634 | C22 | semidirect |
| 15. C2×#14268632 | C22 | semidirect |
| 16. C22×#11744751 | C22 | semidirect |
| 23. #16813555 | C22 | semidirect |
| 24. #16813553 | C22 | semidirect |
| 25. #16813546 | C22 | semidirect |
| 26. #16813543 | C22 | semidirect |
| 27. #16813542 | C22 | semidirect |
| 28. #16813542 | C22 | semidirect |
| 31. C22⋊#11744751 | C22 | semidirect |
| 32. C2×#41×C113 | C22 | semidirect |
| 36. C22⋊Q8×C113 | C22 | semidirect |
| 38. #121×C113 | C22 | semidirect |
| 42. #117×C113 | C22 | semidirect |
| 159. C113 | #3188 | semidirect |
| 160. #525 | D113 | semidirect |
| 171. C2×#41 | C2×D113 | semidirect |
| 180. C22⋊Q8 | C2×D113 | semidirect |
| 186. #121 | C2×D113 | semidirect |
| 190. #117 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813596 | 2 |
| #20298931 | 2 |
| #20298922 | 2 |
| #20298914 | 2 |
| #20298832 | 2 |
| #20298829 | 2 |
| #20298748 | 2 |
| #20298743 | 2 |
| #20298731 | 2 |
| C2×C22⋊#11744751 | 2 |
| #525×C113 | 2 |
| #3188 | 113 |