Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
414 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 116 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 |
|---|---|---|
| 9. #16811673 | C4 | semidirect |
| 10. #16811672 | C4 | semidirect |
| 26. #16810371 | C4 | semidirect |
| 27. #16810371 | C4 | semidirect |
| 28. #16810369 | C4 | semidirect |
| 29. C53×#332 | C4 | semidirect |
| 187. #332 | #6157 | semidirect |
| 191. C53 | #8252 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291504 | 2 |
| #20290508 | 2 |
| #20290098 | 2 |
| #20289921 | 2 |
| #20289612 | 2 |
| #20289607 | 2 |
| #20273371 | 2 |
| #8252 | 53 |