Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
470 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 78 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. #20291408 | C2 | semidirect |
| 2. #20290620 | C2 | semidirect |
| 5. #20289615 | C2 | semidirect |
| 6. #20289597 | C2 | semidirect |
| 28. #16810663 | C4 | semidirect |
| 29. #16810629 | C4 | semidirect |
| 30. #16810627 | C4 | semidirect |
| 32. C53×#428 | C4 | semidirect |
| 240. #428 | #6157 | semidirect |
| 255. C53 | #9348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291408 | 2 |
| #20290620 | 2 |
| #20290152 | 2 |
| #20289992 | 2 |
| #20289615 | 2 |
| #20289597 | 2 |
| #20284657 | 2 |
| #9348 | 53 |