Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
456 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20277820 | C2 | semidirect |
| 3. #20273341 | C2 | semidirect |
| 5. #20272608 | C2 | semidirect |
| 6. #20272607 | C2 | semidirect |
| 9. #16810991 | C4 | semidirect |
| 10. #16810987 | C4 | semidirect |
| 220. C53 | #9442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285115 | 2 |
| #20277820 | 2 |
| #20273341 | 2 |
| #20273223 | 2 |
| #20272608 | 2 |
| #20272607 | 2 |
| C53×#1505 | 2 |
| #9442 | 53 |