Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
316 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 72 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. #20291071 | C2 | semidirect |
| 4. #108×#6157 | C2 | semidirect |
| 5. #20289794 | C2 | semidirect |
| 6. #20289758 | C2 | semidirect |
| 23. #16810439 | C4 | semidirect |
| 24. #16810437 | C4 | semidirect |
| 25. #16810435 | C4 | semidirect |
| 26. C53×#362 | C4 | semidirect |
| 174. #362 | #6157 | semidirect |
| 180. C53 | #13137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291071 | 2 |
| #20291031 | 2 |
| #20290866 | 2 |
| #108×#6157 | 2 |
| #20289794 | 2 |
| #20289758 | 2 |
| #20276463 | 2 |
| #13137 | 53 |