Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1312 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 1312 conjugacy classes of subgroups — too many to draw. Only its 271 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. #20283194 | C2 | semidirect |
| 3. #20276406 | C2 | semidirect |
| 4. #20276398 | C2 | semidirect |
| 5. C53×#2888 | C2 | semidirect |
| 17. #16810607 | C22 | semidirect |
| 19. #16810421 | C22 | semidirect |
| 20. #16810419 | C22 | semidirect |
| 23. C53×#413 | C22 | semidirect |
| 181. #2888 | D53 | semidirect |
| 204. #413 | C2×D53 | semidirect |
| 209. C53 | #33373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288489 | 2 |
| #20283194 | 2 |
| #20276406 | 2 |
| #20276398 | 2 |
| C53×#2888 | 2 |
| #33373 | 53 |