Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
566 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 167 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. #20283326 | C2 | semidirect |
| 2. #20276927 | C2 | semidirect |
| 3. #20276487 | C2 | semidirect |
| 4. C2×#16810436 | C2 | semidirect |
| 5. #20276336 | C2 | semidirect |
| 10. #16810672 | C22 | semidirect |
| 13. #16810445 | C22 | semidirect |
| 15. #16810405 | C22 | semidirect |
| 153. C53 | #33657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283326 | 2 |
| #20276927 | 2 |
| #20276487 | 2 |
| C2×#16810436 | 2 |
| #20276336 | 2 |
| C53×#3058 | 2 |
| #33657 | 53 |