Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
460 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 92 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. #20290474 | C2 | semidirect |
| 4. #20289817 | C2 | semidirect |
| 7. C2×#13133304 | C4 | semidirect |
| 10. #16811628 | C4 | semidirect |
| 13. #16811597 | C4 | semidirect |
| 15. C4×D53⋊C8 | C4 | semidirect |
| 21. #16810421 | C4 | semidirect |
| 22. #16810420 | C4 | semidirect |
| 23. C53×#355 | C4 | semidirect |
| 175. #355 | #6157 | semidirect |
| 179. C53 | #12633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291439 | 2 |
| #20290987 | 2 |
| #20290474 | 2 |
| #20289817 | 2 |
| #20276397 | 2 |
| #12633 | 53 |