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. #20299132 | C2 | semidirect |
| 2. #20299004 | C2 | semidirect |
| 3. #20298985 | C2 | semidirect |
| 4. #20298962 | C2 | semidirect |
| 5. #20298960 | C2 | semidirect |
| 6. #20298849 | C2 | semidirect |
| 7. #20298842 | C2 | semidirect |
| 8. C4×#14268635 | C2 | semidirect |
| 9. C4×#14268632 | C2 | semidirect |
| 10. C4×#14268631 | C2 | semidirect |
| 11. #532×C113 | C2 | semidirect |
| 110. #11744751 | #41 | semidirect |
| 138. C113 | #3171 | semidirect |
| 139. #532 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299132 | 2 |
| #20299004 | 2 |
| #20298985 | 2 |
| #20298962 | 2 |
| #20298960 | 2 |
| #20298849 | 2 |
| #20298842 | 2 |
| C4×#14268635 | 2 |
| C4×#14268632 | 2 |
| C4×#14268631 | 2 |
| #532×C113 | 2 |
| #3171 | 113 |