Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
1504 conjugacy classes of subgroups; only the 770 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 770 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×#16813709 | C2 | direct (N × H) |
| 2. C22×#14268657 | C2 | semidirect |
| 3. C22×#14268656 | C2 | semidirect |
| 4. C22×#14268655 | C2 | semidirect |
| 5. C23×#11744753 | C2 | semidirect |
| 7. #16813709 | C22 | direct (N × H) |
| 8. C2×#14268657 | C22 | semidirect |
| 9. C2×#14268656 | C22 | semidirect |
| 10. C2×#14268655 | C22 | semidirect |
| 14. C22×#11744753 | C22 | semidirect |
| 22. #14268657 | C23 | semidirect |
| 23. #14268656 | C23 | semidirect |
| 24. #14268655 | C23 | semidirect |
| 28. C2×#11744753 | C23 | semidirect |
| 63. C22×C113 | #131 | semidirect |
| 73. C2×C113 | C2×#131 | semidirect |
| 77. C113 | C22×#131 | semidirect |
| 142. C22 | #16813709 | direct (N × H) |
| 151. C2 | C2×#16813709 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813709 | 2 |
| C22×#14268657 | 2 |
| C22×#14268656 | 2 |
| C22×#14268655 | 2 |
| C23×#11744753 | 2 |
| C22×#14268646 | 2 |
| C22×#131 | 113 |