Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 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×#16813648 | C2 | semidirect |
| 2. C4×#14268647 | C2 | semidirect |
| 3. #20298795 | C2 | semidirect |
| 4. #20298790 | C2 | semidirect |
| 5. #20298622 | C2 | semidirect |
| 6. #20298603 | C2 | semidirect |
| 7. C2×#127×C113 | C2 | semidirect |
| 10. C2×#14268635 | C22 | semidirect |
| 11. C2×#14268632 | C22 | semidirect |
| 13. C4×Dic226 | C22 | semidirect |
| 14. C4×D452 | C22 | semidirect |
| 19. C4⋊#11744751 | C22 | semidirect |
| 20. #16813543 | C22 | semidirect |
| 28. #14268647 | D4 | semidirect |
| 78. D452 | C2×D4 | semidirect |
| 82. Dic226 | C2×D4 | semidirect |
| 94. C4×C113 | AGL(1,ℤ/8) | semidirect |
| 105. C113 | #3038 | semidirect |
| 107. C2×#127 | D113 | semidirect |
| 201. C4 | #16813648 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813648 | 2 |
| C4×#14268647 | 2 |
| #20298795 | 2 |
| #20298790 | 2 |
| #20298622 | 2 |
| #20298603 | 2 |
| C2×#127×C113 | 2 |
| #3038 | 113 |