Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
466 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 98 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. #20290826 | C2 | semidirect |
| 4. #20290508 | C2 | semidirect |
| 5. #20289594 | C2 | semidirect |
| 6. #20289544 | C2 | semidirect |
| 23. #16810367 | C4 | semidirect |
| 24. #16810366 | C4 | semidirect |
| 25. #16810366 | C4 | semidirect |
| 26. C53×#331 | C4 | semidirect |
| 243. #331 | #6157 | semidirect |
| 244. C53 | #9563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290882 | 2 |
| #20290843 | 2 |
| #20290826 | 2 |
| #20290508 | 2 |
| #20289594 | 2 |
| #20289544 | 2 |
| #331×D53 | 2 |
| #9563 | 53 |