Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 386 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. #20299203 | C2 | semidirect |
| 2. #20298997 | C2 | semidirect |
| 3. #20298974 | C2 | semidirect |
| 4. #20298964 | C2 | semidirect |
| 5. #20298962 | C2 | semidirect |
| 6. #20298849 | C2 | semidirect |
| 7. #20298832 | C2 | semidirect |
| 8. #20298708 | C2 | semidirect |
| 9. C4×#14268632 | C2 | semidirect |
| 10. #20298554 | C2 | semidirect |
| 11. #540×C113 | C2 | semidirect |
| 115. C113 | #3176 | semidirect |
| 117. #540 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299203 | 2 |
| #20298997 | 2 |
| #20298974 | 2 |
| #20298964 | 2 |
| #20298962 | 2 |
| #20298849 | 2 |
| #20298832 | 2 |
| #20298708 | 2 |
| C4×#14268632 | 2 |
| #20298554 | 2 |
| #540×C113 | 2 |
| #3176 | 113 |