Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
468 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 74 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. #20291603 | C2 | semidirect |
| 2. #20290247 | C2 | semidirect |
| 3. #20290040 | C2 | semidirect |
| 4. #20289975 | C2 | semidirect |
| 5. #20289620 | C2 | semidirect |
| 6. #20289573 | C2 | semidirect |
| 257. C53 | #9529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291603 | 2 |
| #20290247 | 2 |
| #20290040 | 2 |
| #20289975 | 2 |
| #20289620 | 2 |
| #20289573 | 2 |
| #20284801 | 2 |
| #9529 | 53 |