Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
452 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20283885 | C2 | semidirect |
| 3. #20275547 | C2 | semidirect |
| 4. #20273185 | C2 | semidirect |
| 5. #20272608 | C2 | semidirect |
| 6. #20272606 | C2 | semidirect |
| 7. C53×#1500 | C2 | semidirect |
| 9. #16811033 | C4 | semidirect |
| 10. #16811013 | C4 | semidirect |
| 11. #16810989 | C4 | semidirect |
| 12. #16810982 | C4 | semidirect |
| 213. #1500 | D53 | semidirect |
| 250. C53 | #8997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285311 | 2 |
| #20283885 | 2 |
| #20275547 | 2 |
| #20273185 | 2 |
| #20272608 | 2 |
| #20272606 | 2 |
| C53×#1500 | 2 |
| #8997 | 53 |