Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
362 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20299308 | C2 | semidirect |
| 2. #20298952 | C2 | semidirect |
| 3. #20298944 | C2 | semidirect |
| 4. #20298898 | C2 | semidirect |
| 5. #20298893 | C2 | semidirect |
| 6. #20298810 | C2 | semidirect |
| 8. Q8×#11744751 | C2 | semidirect |
| 9. C4×#14268634 | C2 | semidirect |
| 10. C4×#14268632 | C2 | semidirect |
| 11. #559×C113 | C2 | semidirect |
| 123. C113 | #3361 | semidirect |
| 124. #559 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299308 | 2 |
| #20298952 | 2 |
| #20298944 | 2 |
| #20298898 | 2 |
| #20298893 | 2 |
| #20298810 | 2 |
| #20298790 | 2 |
| Q8×#11744751 | 2 |
| C4×#14268634 | 2 |
| C4×#14268632 | 2 |
| #559×C113 | 2 |
| #3361 | 113 |