Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
504 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 93 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. #20283769 | C2 | semidirect |
| 3. #20273220 | C2 | semidirect |
| 4. C2×#16810357 | C2 | semidirect |
| 5. #20272602 | C2 | semidirect |
| 6. #20272557 | C2 | semidirect |
| 7. C53×#1471 | C2 | semidirect |
| 9. #16810958 | C4 | semidirect |
| 11. #16810941 | C4 | semidirect |
| 14. #16810774 | C4 | semidirect |
| 16. #16810757 | C4 | semidirect |
| 240. #1471 | D53 | semidirect |
| 280. C53 | #9264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285480 | 2 |
| #20283769 | 2 |
| #20273220 | 2 |
| C2×#16810357 | 2 |
| #20272602 | 2 |
| #20272557 | 2 |
| C53×#1471 | 2 |
| #9264 | 53 |