Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
528 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 189 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. #20299072 | C2 | semidirect |
| 3. #20298708 | C2 | semidirect |
| 4. C4×#14268632 | C2 | semidirect |
| 5. #20298634 | C2 | semidirect |
| 6. #20298603 | C2 | semidirect |
| 7. #20298602 | C2 | semidirect |
| 8. #20298554 | C2 | semidirect |
| 9. #518×C113 | C2 | semidirect |
| 11. C2×#14268632 | C4 | semidirect |
| 16. C4×D452 | C22 | semidirect |
| 20. #16813555 | C22 | semidirect |
| 21. #16813553 | C22 | semidirect |
| 22. #16813543 | C22 | semidirect |
| 23. #16813542 | C22 | semidirect |
| 24. #16813533 | C22 | semidirect |
| 25. C4×#11744751 | C22 | semidirect |
| 28. C4×D4×C113 | C22 | semidirect |
| 35. C2×D452 | C2×C4 | semidirect |
| 38. #14268632 | C2×C4 | semidirect |
| 39. #14268632 | C2×C4 | semidirect |
| 41. C2×#11744751 | C2×C4 | semidirect |
| 52. C2×D4×C113 | C2×C4 | semidirect |
| 109. C113 | #2948 | semidirect |
| 112. #518 | D113 | semidirect |
| 129. C4×D4 | C2×D113 | semidirect |
| 149. C2×D4 | C4×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14268632 | 2 |
| #20299072 | 2 |
| #20298708 | 2 |
| C4×#14268632 | 2 |
| #20298634 | 2 |
| #20298603 | 2 |
| #20298602 | 2 |
| #20298554 | 2 |
| #518×C113 | 2 |
| #2948 | 113 |