Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 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. #20299155 | C2 | semidirect |
| 3. #20298971 | C2 | semidirect |
| 4. #20298945 | C2 | semidirect |
| 5. #20298799 | C2 | semidirect |
| 6. #20298751 | C2 | semidirect |
| 7. #431×C113 | C2 | semidirect |
| 11. C2×#14268636 | C22 | semidirect |
| 12. #16813622 | C22 | semidirect |
| 13. #16813622 | C22 | semidirect |
| 22. C4×Dic226 | C22 | semidirect |
| 24. #16813544 | C22 | semidirect |
| 26. C4⋊C8×C113 | C22 | semidirect |
| 28. C4×C8×C113 | C22 | semidirect |
| 65. C2×C4×C113 | SD16 | semidirect |
| 105. C113 | #3208 | semidirect |
| 112. #431 | D113 | semidirect |
| 130. C4⋊C8 | C2×D113 | semidirect |
| 133. C4×C8 | C2×D113 | semidirect |
| 180. C2×C4 | #14268636 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299155 | 2 |
| C2×#16813619 | 2 |
| #20298971 | 2 |
| #20298945 | 2 |
| #20298799 | 2 |
| #20298751 | 2 |
| #431×C113 | 2 |
| #3208 | 113 |