Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
500 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 204 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. #20299626 | C2 | semidirect |
| 2. #20299614 | C2 | semidirect |
| 3. #20299566 | C2 | semidirect |
| 5. C2×#14268655 | C22 | semidirect |
| 6. C4⋊#11744753 | C22 | semidirect |
| 7. #16813679 | C22 | semidirect |
| 9. C4×#11744753 | C22 | semidirect |
| 20. C2×D452 | C8 | semidirect |
| 36. C22×D113 | C2×C8 | semidirect |
| 39. C2×C4×C113 | C2×C8 | semidirect |
| 47. D452 | C2×C8 | semidirect |
| 70. C113 | #2972 | semidirect |
| 117. C2×C4 | #14268655 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299626 | 2 |
| #20299614 | 2 |
| #20299566 | 2 |
| C2×#16813584 | 2 |
| #2972 | 113 |