Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
408 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 408 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. #20299313 | C2 | semidirect |
| 2. #20298944 | C2 | semidirect |
| 3. #20298919 | C2 | semidirect |
| 4. #20298893 | C2 | semidirect |
| 5. #20298832 | C2 | semidirect |
| 6. #20298790 | C2 | semidirect |
| 7. #20298743 | C2 | semidirect |
| 8. C4×#14268634 | C2 | semidirect |
| 9. D4×#11744751 | C2 | semidirect |
| 10. #20298594 | C2 | semidirect |
| 11. #550×C113 | C2 | semidirect |
| 133. C113 | #3305 | semidirect |
| 135. #550 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299313 | 2 |
| #20298944 | 2 |
| #20298919 | 2 |
| #20298893 | 2 |
| #20298832 | 2 |
| #20298790 | 2 |
| #20298743 | 2 |
| C4×#14268634 | 2 |
| D4×#11744751 | 2 |
| #20298594 | 2 |
| #550×C113 | 2 |
| #3305 | 113 |