Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
438 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. #20273247 | C2 | semidirect |
| 5. #20273080 | C2 | semidirect |
| 6. #20272591 | C2 | semidirect |
| 7. C53×#1306 | C2 | semidirect |
| 11. #16810959 | C4 | semidirect |
| 12. #16810942 | C4 | semidirect |
| 16. #16810781 | C4 | semidirect |
| 17. #16810764 | C4 | semidirect |
| 215. #1306 | D53 | semidirect |
| 251. C53 | #9331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285547 | 2 |
| #20283775 | 2 |
| #20273269 | 2 |
| #20273247 | 2 |
| #20273080 | 2 |
| #20272591 | 2 |
| C53×#1306 | 2 |
| #9331 | 53 |