Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
500 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 105 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. #20277682 | C2 | semidirect |
| 5. #20273109 | C2 | semidirect |
| 6. #20272616 | C2 | semidirect |
| 7. C53×#1286 | C2 | semidirect |
| 12. #16810834 | C4 | semidirect |
| 13. #16810824 | C4 | semidirect |
| 198. #1286 | D53 | semidirect |
| 226. C53 | #9182 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284189 | 2 |
| #20277682 | 2 |
| #20273274 | 2 |
| #20273211 | 2 |
| #20273109 | 2 |
| #20272616 | 2 |
| C53×#1286 | 2 |
| #9182 | 53 |