Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
504 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 125 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×#16813643 | C2 | semidirect |
| 2. #20299270 | C2 | semidirect |
| 3. #20299268 | C2 | semidirect |
| 4. #20298974 | C2 | semidirect |
| 5. #20298833 | C2 | semidirect |
| 6. #20298799 | C2 | semidirect |
| 7. #20298744 | C2 | semidirect |
| 8. #20298742 | C2 | semidirect |
| 9. C4×#14268637 | C2 | semidirect |
| 10. #20298663 | C2 | semidirect |
| 11. #460×C113 | C2 | semidirect |
| 58. #14268637 | D4 | semidirect |
| 130. C4×C113 | #135 | semidirect |
| 143. C113 | #3287 | semidirect |
| 150. #460 | D113 | semidirect |
| 276. C4 | #16813643 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813643 | 2 |
| #20299270 | 2 |
| #20299268 | 2 |
| #20298974 | 2 |
| #20298833 | 2 |
| #20298799 | 2 |
| #20298744 | 2 |
| #20298742 | 2 |
| C4×#14268637 | 2 |
| #20298663 | 2 |
| #460×C113 | 2 |
| #3287 | 113 |