Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
390 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20299153 | C2 | semidirect |
| 3. #20298990 | C2 | semidirect |
| 4. #20298958 | C2 | semidirect |
| 5. #20298957 | C2 | semidirect |
| 6. #20298806 | C2 | semidirect |
| 7. #20298796 | C2 | semidirect |
| 8. #20298759 | C2 | semidirect |
| 9. #20298757 | C2 | semidirect |
| 10. #20298653 | C2 | semidirect |
| 11. #497×C113 | C2 | semidirect |
| 142. C113 | #3216 | semidirect |
| 146. #497 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299153 | 2 |
| #20299147 | 2 |
| #20298990 | 2 |
| #20298958 | 2 |
| #20298957 | 2 |
| #20298806 | 2 |
| #20298796 | 2 |
| #20298759 | 2 |
| #20298757 | 2 |
| #20298653 | 2 |
| #497×C113 | 2 |
| #3216 | 113 |