Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
420 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 139 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. #20299252 | C2 | semidirect |
| 2. #20299001 | C2 | semidirect |
| 3. #20298911 | C2 | semidirect |
| 4. #20298909 | C2 | semidirect |
| 5. #20298878 | C2 | semidirect |
| 6. #20298875 | C2 | semidirect |
| 7. #20298832 | C2 | semidirect |
| 8. C4×#14268632 | C2 | semidirect |
| 9. D4×#11744751 | C2 | semidirect |
| 10. C2×#16813555 | C2 | semidirect |
| 11. #547×C113 | C2 | semidirect |
| 82. D4×C113 | D8 | semidirect |
| 103. #11744751 | #41 | semidirect |
| 130. C113 | #3334 | semidirect |
| 132. #547 | D113 | semidirect |
| 216. D4 | #14268632 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299252 | 2 |
| #20299001 | 2 |
| #20298911 | 2 |
| #20298909 | 2 |
| #20298878 | 2 |
| #20298875 | 2 |
| #20298832 | 2 |
| C4×#14268632 | 2 |
| D4×#11744751 | 2 |
| C2×#16813555 | 2 |
| #547×C113 | 2 |
| #3334 | 113 |