Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
364 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 129 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. #20299155 | C2 | semidirect |
| 3. #20299007 | C2 | semidirect |
| 4. #20298992 | C2 | semidirect |
| 5. #20298967 | C2 | semidirect |
| 6. #20298958 | C2 | semidirect |
| 7. #20298856 | C2 | semidirect |
| 9. C4×Dic452 | C2 | semidirect |
| 10. C4×#14268636 | C2 | semidirect |
| 11. C4×M16×C113 | C2 | semidirect |
| 130. C113 | #3172 | semidirect |
| 141. C4×M16 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299155 | 2 |
| #20299132 | 2 |
| #20299007 | 2 |
| #20298992 | 2 |
| #20298967 | 2 |
| #20298958 | 2 |
| #20298856 | 2 |
| #20298844 | 2 |
| C4×Dic452 | 2 |
| C4×#14268636 | 2 |
| C4×M16×C113 | 2 |
| #3172 | 113 |