Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#14268634 | C2 | semidirect |
| 2. C2×#16813629 | C2 | semidirect |
| 4. #20298846 | C2 | semidirect |
| 5. #20298829 | C2 | semidirect |
| 6. #20298634 | C2 | semidirect |
| 7. #20298607 | C2 | semidirect |
| 8. #20298602 | C2 | semidirect |
| 9. #536×C113 | C2 | semidirect |
| 16. C2×#14268631 | C22 | semidirect |
| 18. C22×#11744751 | C22 | semidirect |
| 24. #16813555 | C22 | semidirect |
| 25. #16813553 | C22 | semidirect |
| 26. #16813546 | C22 | semidirect |
| 33. C22⋊Q8×C113 | C22 | semidirect |
| 46. C2×#11744751 | D4 | semidirect |
| 121. C113 | #3057 | semidirect |
| 124. #536 | D113 | semidirect |
| 147. C22⋊Q8 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14268634 | 2 |
| C2×#16813629 | 2 |
| #20299162 | 2 |
| #20298846 | 2 |
| #20298829 | 2 |
| #20298634 | 2 |
| #20298607 | 2 |
| #20298602 | 2 |
| #536×C113 | 2 |
| #3057 | 113 |