Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
476 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 25. #16810372 | C4 | semidirect |
| 26. #16810371 | C4 | semidirect |
| 27. #16810371 | C4 | semidirect |
| 28. C53×#333 | C4 | semidirect |
| 224. #333 | #6157 | semidirect |
| 225. C53 | #8927 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291248 | 2 |
| #20290842 | 2 |
| #20290827 | 2 |
| #20290826 | 2 |
| #20289549 | 2 |
| #333×D53 | 2 |
| #8927 | 53 |