Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
426 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 426 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. #20299269 | C2 | semidirect |
| 2. D4×Dic226 | C2 | semidirect |
| 3. #20298945 | C2 | semidirect |
| 4. #20298943 | C2 | semidirect |
| 5. #20298878 | C2 | semidirect |
| 6. #20298877 | C2 | semidirect |
| 7. #20298793 | C2 | semidirect |
| 8. #20298791 | C2 | semidirect |
| 9. C8×Dic226 | C2 | semidirect |
| 10. #20298678 | C2 | semidirect |
| 11. C4×D8×C113 | C2 | semidirect |
| 81. D4×C113 | #41 | semidirect |
| 102. Dic226 | D8 | semidirect |
| 132. C113 | #3358 | semidirect |
| 143. C4×D8 | D113 | semidirect |
| 222. D4 | #14268647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299269 | 2 |
| D4×Dic226 | 2 |
| #20298945 | 2 |
| #20298943 | 2 |
| #20298878 | 2 |
| #20298877 | 2 |
| #20298793 | 2 |
| #20298791 | 2 |
| C8×Dic226 | 2 |
| #20298678 | 2 |
| C4×D8×C113 | 2 |
| #3358 | 113 |