Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
470 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20283373 | C2 | semidirect |
| 5. #20272621 | C2 | semidirect |
| 6. #20272603 | C2 | semidirect |
| 7. C53×#1825 | C2 | semidirect |
| 16. #16810666 | C4 | semidirect |
| 17. #16810666 | C4 | semidirect |
| 19. #16810627 | C4 | semidirect |
| 20. #16810627 | C4 | semidirect |
| 217. #1825 | D53 | semidirect |
| 255. C53 | #9348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284655 | 2 |
| #20283373 | 2 |
| #20273282 | 2 |
| #20273074 | 2 |
| #20272621 | 2 |
| #20272603 | 2 |
| C53×#1825 | 2 |
| #9348 | 53 |