Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #20299129 | C2 | semidirect |
| 2. #20298999 | C2 | semidirect |
| 3. #20298981 | C2 | semidirect |
| 4. #20298951 | C2 | semidirect |
| 5. #20298839 | C2 | semidirect |
| 6. #20298825 | C2 | semidirect |
| 7. #20298692 | C2 | semidirect |
| 8. #20298689 | C2 | semidirect |
| 9. D8×Dic113 | C2 | semidirect |
| 10. C2×C8×Dic113 | C2 | semidirect |
| 119. C113 | #3168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299129 | 2 |
| #20298999 | 2 |
| #20298981 | 2 |
| #20298951 | 2 |
| #20298839 | 2 |
| #20298825 | 2 |
| #20298692 | 2 |
| #20298689 | 2 |
| D8×Dic113 | 2 |
| C2×C8×Dic113 | 2 |
| #466×C113 | 2 |
| #3168 | 113 |