Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
564 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20277795 | C2 | semidirect |
| 4. #20273288 | C2 | semidirect |
| 5. #20272594 | C2 | semidirect |
| 6. #20272562 | C2 | semidirect |
| 9. #16810953 | C4 | semidirect |
| 12. #16810774 | C4 | semidirect |
| 125. C22⋊Dic53 | SD16 | semidirect |
| 274. C53 | #9278 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285472 | 2 |
| #20277795 | 2 |
| #20275552 | 2 |
| #20273288 | 2 |
| #20272594 | 2 |
| #20272562 | 2 |
| C2×C53×#327 | 2 |
| #9278 | 53 |