Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
654 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 16. #16810651 | C4 | semidirect |
| 17. #16810650 | C4 | semidirect |
| 18. #16810649 | C4 | semidirect |
| 21. C53×#424 | C4 | semidirect |
| 190. #424 | #6157 | semidirect |
| 195. C53 | #11236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291368 | 2 |
| #20290413 | 2 |
| #20290401 | 2 |
| #20290387 | 2 |
| #424×D53 | 2 |
| #11236 | 53 |