Finite Group DatabasebetaFinite Group DatabasebetaOrder 14656.
234 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20300983 | C2 | semidirect |
| 2. #20300981 | C2 | semidirect |
| 3. #20300978 | C2 | semidirect |
| 4. #20300974 | C2 | semidirect |
| 5. #20300973 | C2 | semidirect |
| 6. #20300970 | C2 | semidirect |
| 7. #20300966 | C2 | semidirect |
| 9. C4×Dic458 | C2 | semidirect |
| 10. C4×D916 | C2 | semidirect |
| 11. C4×C22⋊D229 | C2 | semidirect |
| 12. C4×C22⋊D229 | C2 | semidirect |
| 13. #20300945 | C2 | semidirect |
| 14. C42×D229 | C2 | semidirect |
| 15. #117×C229 | C2 | semidirect |
| 103. C229 | #529 | semidirect |
| 118. #117 | D229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20300983 | 2 |
| #20300981 | 2 |
| #20300978 | 2 |
| #20300974 | 2 |
| #20300973 | 2 |
| #20300970 | 2 |
| #20300966 | 2 |
| #20300961 | 2 |
| C4×Dic458 | 2 |
| C4×D916 | 2 |
| C4×C22⋊D229 | 2 |
| #20300945 | 2 |
| C42×D229 | 2 |
| #117×C229 | 2 |
| #529 | 229 |