Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
430 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 3. #20273432 | C2 | semidirect |
| 5. #20272585 | C2 | semidirect |
| 6. #20272571 | C2 | semidirect |
| 7. C53×#1987 | C2 | semidirect |
| 9. #16811015 | C4 | semidirect |
| 10. #16810991 | C4 | semidirect |
| 186. #1987 | D53 | semidirect |
| 222. C53 | #9376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285742 | 2 |
| #20283851 | 2 |
| #20273432 | 2 |
| #20273238 | 2 |
| #20272585 | 2 |
| #20272571 | 2 |
| C53×#1987 | 2 |
| #9376 | 53 |