Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
420 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 420 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 |
|---|---|---|
| 3. #20274761 | C2 | semidirect |
| 4. #20272845 | C2 | semidirect |
| 5. C53×#1813 | C2 | semidirect |
| 6. C22×#11719912 | C4 | semidirect |
| 13. #16810651 | C4 | semidirect |
| 16. #16810586 | C4 | semidirect |
| 17. #16810578 | C4 | semidirect |
| 182. #1813 | D53 | semidirect |
| 210. C53 | #12806 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283416 | 2 |
| #20276357 | 2 |
| #20274761 | 2 |
| #20272845 | 2 |
| C53×#1813 | 2 |
| #12806 | 53 |