Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
504 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20283771 | C2 | semidirect |
| 3. C2×#16810356 | C2 | semidirect |
| 4. #20273076 | C2 | semidirect |
| 5. #20272602 | C2 | semidirect |
| 6. #20272558 | C2 | semidirect |
| 7. C53×#1504 | C2 | semidirect |
| 9. #16810956 | C4 | semidirect |
| 11. #16810939 | C4 | semidirect |
| 14. #16810773 | C4 | semidirect |
| 16. #16810756 | C4 | semidirect |
| 238. #1504 | D53 | semidirect |
| 280. C53 | #9264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285476 | 2 |
| #20283771 | 2 |
| C2×#16810356 | 2 |
| #20273076 | 2 |
| #20272602 | 2 |
| #20272558 | 2 |
| C53×#1504 | 2 |
| #9264 | 53 |