Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
516 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 516 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 |
|---|---|---|
| 2. #20283836 | C2 | semidirect |
| 3. #20275543 | C2 | semidirect |
| 4. C4×#13133145 | C2 | semidirect |
| 5. #20273131 | C2 | semidirect |
| 6. #20272606 | C2 | semidirect |
| 7. C53×#1276 | C2 | semidirect |
| 11. #16810919 | C4 | semidirect |
| 12. #16810914 | C4 | semidirect |
| 13. #16810824 | C4 | semidirect |
| 14. #16810819 | C4 | semidirect |
| 169. D212 | #104 | semidirect |
| 217. #1276 | D53 | semidirect |
| 249. C53 | #8969 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284776 | 2 |
| #20283836 | 2 |
| #20275543 | 2 |
| C4×#13133145 | 2 |
| #20273131 | 2 |
| #20272606 | 2 |
| C53×#1276 | 2 |
| #8969 | 53 |