Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
402 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. #20283820 | C2 | semidirect |
| 4. #20273267 | C2 | semidirect |
| 6. #20272580 | C2 | semidirect |
| 7. C53×#1291 | C2 | semidirect |
| 10. #16811028 | C4 | semidirect |
| 11. #16810996 | C4 | semidirect |
| 12. #16810974 | C4 | semidirect |
| 13. #16810970 | C4 | semidirect |
| 156. #1291 | D53 | semidirect |
| 182. C53 | #9418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285433 | 2 |
| #20283820 | 2 |
| #20273349 | 2 |
| #20273267 | 2 |
| #20273263 | 2 |
| #20272580 | 2 |
| C53×#1291 | 2 |
| #9418 | 53 |