Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20299148 | C2 | semidirect |
| 2. #20299132 | C2 | semidirect |
| 3. #20298992 | C2 | semidirect |
| 4. #20298987 | C2 | semidirect |
| 5. #20298967 | C2 | semidirect |
| 6. #20298963 | C2 | semidirect |
| 7. #20298821 | C2 | semidirect |
| 8. #20298814 | C2 | semidirect |
| 9. #20298762 | C2 | semidirect |
| 10. #20298745 | C2 | semidirect |
| 11. #432×C113 | C2 | semidirect |
| 141. C113 | #3219 | semidirect |
| 152. #432 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299148 | 2 |
| #20299132 | 2 |
| #20298992 | 2 |
| #20298987 | 2 |
| #20298967 | 2 |
| #20298963 | 2 |
| #20298821 | 2 |
| #20298814 | 2 |
| #20298762 | 2 |
| #20298745 | 2 |
| #432×C113 | 2 |
| #3219 | 113 |