Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
428 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 1. #20291403 | C2 | semidirect |
| 2. #20290185 | C2 | semidirect |
| 3. #20290049 | C2 | semidirect |
| 4. #20290035 | C2 | semidirect |
| 5. #20289608 | C2 | semidirect |
| 6. #20289581 | C2 | semidirect |
| 229. C53 | #9313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291403 | 2 |
| #20290185 | 2 |
| #20290049 | 2 |
| #20290035 | 2 |
| #20289608 | 2 |
| #20289581 | 2 |
| #20284865 | 2 |
| #9313 | 53 |