Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
374 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 374 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 |
|---|---|---|
| 2. #20299001 | C2 | semidirect |
| 3. #20298931 | C2 | semidirect |
| 4. #20298922 | C2 | semidirect |
| 5. #20298883 | C2 | semidirect |
| 6. #20298875 | C2 | semidirect |
| 7. #20298846 | C2 | semidirect |
| 8. C4×#14268634 | C2 | semidirect |
| 9. #20298676 | C2 | semidirect |
| 10. #20298641 | C2 | semidirect |
| 11. #556×C113 | C2 | semidirect |
| 99. #11744751 | #41 | semidirect |
| 123. C113 | #3353 | semidirect |
| 124. #556 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299252 | 2 |
| #20299001 | 2 |
| #20298931 | 2 |
| #20298922 | 2 |
| #20298883 | 2 |
| #20298875 | 2 |
| #20298846 | 2 |
| C4×#14268634 | 2 |
| #20298676 | 2 |
| #20298641 | 2 |
| #556×C113 | 2 |
| #3353 | 113 |