Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
460 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20275692 | C2 | semidirect |
| 4. #20273474 | C2 | semidirect |
| 5. #20273171 | C2 | semidirect |
| 7. C53×#1744 | C2 | semidirect |
| 10. #16811021 | C4 | semidirect |
| 11. #16810996 | C4 | semidirect |
| 12. #16810974 | C4 | semidirect |
| 13. #16810970 | C4 | semidirect |
| 163. #1744 | D53 | semidirect |
| 191. C53 | #9854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285274 | 2 |
| #20275692 | 2 |
| #20275543 | 2 |
| #20273474 | 2 |
| #20273171 | 2 |
| #20273167 | 2 |
| C53×#1744 | 2 |
| #9854 | 53 |