Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
390 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 86 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. #20291057 | C2 | semidirect |
| 4. #20290635 | C2 | semidirect |
| 5. #20289788 | C2 | semidirect |
| 6. #20289779 | C2 | semidirect |
| 20. #16810735 | C4 | semidirect |
| 21. #16810731 | C4 | semidirect |
| 22. #16810729 | C4 | semidirect |
| 28. C53×#442 | C4 | semidirect |
| 188. #442 | #6157 | semidirect |
| 204. C53 | #12828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291057 | 2 |
| #20291036 | 2 |
| #20291030 | 2 |
| #20290635 | 2 |
| #20289788 | 2 |
| #20289779 | 2 |
| #20283597 | 2 |
| #12828 | 53 |