Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
644 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 644 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 |
|---|---|---|
| 3. #20274649 | C2 | semidirect |
| 4. #20274638 | C2 | semidirect |
| 5. #20272621 | C2 | semidirect |
| 6. #20272591 | C2 | semidirect |
| 11. #16810778 | C4 | semidirect |
| 13. #16810761 | C4 | semidirect |
| 283. C53 | #9519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283948 | 2 |
| #20283763 | 2 |
| #20274649 | 2 |
| #20274638 | 2 |
| #20272621 | 2 |
| #20272591 | 2 |
| C53×#1513 | 2 |
| #9519 | 53 |