Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 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. #20298974 | C2 | semidirect |
| 4. #20298832 | C2 | semidirect |
| 5. #20298798 | C2 | semidirect |
| 6. #20298795 | C2 | semidirect |
| 7. #20298743 | C2 | semidirect |
| 8. #20298741 | C2 | semidirect |
| 9. C4×#14268637 | C2 | semidirect |
| 10. D4×#11744751 | C2 | semidirect |
| 11. #550×C113 | C2 | semidirect |
| 51. #14268637 | D4 | semidirect |
| 131. C4×C113 | #135 | semidirect |
| 143. C113 | #3287 | semidirect |
| 146. #550 | D113 | semidirect |
| 276. 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 |
| #20298974 | 2 |
| #20298832 | 2 |
| #20298798 | 2 |
| #20298795 | 2 |
| #20298743 | 2 |
| #20298741 | 2 |
| C4×#14268637 | 2 |
| D4×#11744751 | 2 |
| #550×C113 | 2 |
| #3287 | 113 |