Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#16813642 | C2 | semidirect |
| 2. #20299269 | C2 | semidirect |
| 3. #20298972 | C2 | semidirect |
| 4. #20298829 | C2 | semidirect |
| 5. #20298805 | C2 | semidirect |
| 6. #20298793 | C2 | semidirect |
| 7. #20298758 | C2 | semidirect |
| 8. #20298743 | C2 | semidirect |
| 9. C4×#14268635 | C2 | semidirect |
| 10. D4×#11744751 | C2 | semidirect |
| 11. #547×C113 | C2 | semidirect |
| 52. #14268635 | D4 | semidirect |
| 129. C4×C113 | #135 | semidirect |
| 141. C113 | #3284 | semidirect |
| 144. #547 | D113 | semidirect |
| 272. C4 | #16813642 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813642 | 2 |
| #20299269 | 2 |
| #20298972 | 2 |
| #20298829 | 2 |
| #20298805 | 2 |
| #20298793 | 2 |
| #20298758 | 2 |
| #20298743 | 2 |
| C4×#14268635 | 2 |
| D4×#11744751 | 2 |
| #547×C113 | 2 |
| #3284 | 113 |