Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
434 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20274763 | C2 | semidirect |
| 5. #20274759 | C2 | semidirect |
| 6. #20272844 | C2 | semidirect |
| 7. C53×#1395 | C2 | semidirect |
| 9. C22×C8×D53 | C4 | semidirect |
| 17. #16810649 | C4 | semidirect |
| 20. #16810586 | C4 | semidirect |
| 21. #16810581 | C4 | semidirect |
| 208. #1395 | D53 | semidirect |
| 238. C53 | #12805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283412 | 2 |
| #20276357 | 2 |
| #20276354 | 2 |
| #20274763 | 2 |
| #20274759 | 2 |
| #20272844 | 2 |
| C53×#1395 | 2 |
| #12805 | 53 |