Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
444 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 113 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. #20299143 | C2 | semidirect |
| 2. C2×#16813611 | C2 | semidirect |
| 3. #20298984 | C2 | semidirect |
| 4. #20298959 | C2 | semidirect |
| 5. #20298816 | C2 | semidirect |
| 6. #20298815 | C2 | semidirect |
| 7. #20298737 | C2 | semidirect |
| 8. #20298734 | C2 | semidirect |
| 9. #20298731 | C2 | semidirect |
| 10. #20298652 | C2 | semidirect |
| 11. #448×C113 | C2 | semidirect |
| 14. C2×#14268634 | C22 | semidirect |
| 17. #16813621 | C22 | semidirect |
| 18. #16813618 | C22 | semidirect |
| 26. D4×Dic113 | C22 | semidirect |
| 27. #16813584 | C22 | semidirect |
| 32. #16813551 | C22 | semidirect |
| 33. #16813546 | C22 | semidirect |
| 37. #16813532 | C22 | semidirect |
| 39. C2×SD16×C113 | C22 | semidirect |
| 41. #103×C113 | C22 | semidirect |
| 153. C113 | #3213 | semidirect |
| 161. #448 | D113 | semidirect |
| 169. C2×SD16 | C2×D113 | semidirect |
| 190. #103 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299143 | 2 |
| C2×#16813611 | 2 |
| #20298984 | 2 |
| #20298959 | 2 |
| #20298816 | 2 |
| #20298815 | 2 |
| #20298737 | 2 |
| #20298734 | 2 |
| #20298731 | 2 |
| #20298652 | 2 |
| #448×C113 | 2 |
| #3213 | 113 |