Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1312 conjugacy classes of subgroups; only the 311 normal subgroups are shown.
This group has 1312 conjugacy classes of subgroups — too many to draw. Only its 311 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. #20283194 | C2 | semidirect |
| 2. #20276407 | C2 | semidirect |
| 3. #20276400 | C2 | semidirect |
| 6. #16810607 | C22 | semidirect |
| 8. #16810422 | C22 | semidirect |
| 9. #16810420 | C22 | semidirect |
| 159. C53 | #33373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283194 | 2 |
| #20276407 | 2 |
| #20276400 | 2 |
| C53×#3498 | 2 |
| #33373 | 53 |