Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
478 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 93 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. #20273079 | C2 | semidirect |
| 5. #20272603 | C2 | semidirect |
| 6. #20272558 | C2 | semidirect |
| 7. C2×C53×#328 | C2 | semidirect |
| 10. #16810953 | C4 | semidirect |
| 11. #16810936 | C4 | semidirect |
| 15. #16810779 | C4 | semidirect |
| 16. #16810762 | C4 | semidirect |
| 228. C2×#328 | D53 | semidirect |
| 268. C53 | #9263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285496 | 2 |
| #20283769 | 2 |
| #20273217 | 2 |
| #20273079 | 2 |
| #20272603 | 2 |
| #20272558 | 2 |
| C2×C53×#328 | 2 |
| #9263 | 53 |