Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
498 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 71 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. #20276380 | C2 | semidirect |
| 3. #20272867 | C2 | semidirect |
| 4. C53×#1525 | C2 | semidirect |
| 5. #16811459 | C4 | semidirect |
| 7. #16810805 | C4 | semidirect |
| 12. #16810607 | C4 | semidirect |
| 14. #16810418 | C22 | semidirect |
| 19. C53×#329 | C22 | semidirect |
| 171. #1525 | D53 | semidirect |
| 193. #329 | C2×D53 | semidirect |
| 194. C53 | #13568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284063 | 2 |
| #20276380 | 2 |
| #20272867 | 2 |
| C53×#1525 | 2 |
| #13568 | 53 |