Finite Group DatabasebetaFinite Group DatabasebetaOrder 14656.
106 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 47 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 |
|---|---|---|
| 2. #20300994 | C2 | semidirect |
| 3. #20300923 | C2 | semidirect |
| 4. #20300915 | C2 | semidirect |
| 5. #20300914 | C2 | semidirect |
| 6. C8×Dic229 | C2 | semidirect |
| 7. #131×C229 | C2 | semidirect |
| 9. #16814656 | C4 | semidirect |
| 10. #16814654 | C4 | semidirect |
| 11. #16814653 | C4 | semidirect |
| 12. #16814651 | C4 | semidirect |
| 51. C229 | #443 | semidirect |
| 55. #131 | D229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20301008 | 2 |
| #20300994 | 2 |
| #20300923 | 2 |
| #20300915 | 2 |
| #20300914 | 2 |
| C8×Dic229 | 2 |
| #131×C229 | 2 |
| #443 | 229 |