Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
3246 conjugacy classes of subgroups; only the 491 normal subgroups are shown.
This group has 3246 conjugacy classes of subgroups — too many to draw. Only its 491 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. #20272964 | C2 | semidirect |
| 3. #20272938 | C2 | semidirect |
| 8. C2×#13133124 | C22 | semidirect |
| 12. C22×C22⋊C4×C53 | C4 | semidirect |
| 121. C22×C22⋊C4 | Dic53 | semidirect |
| 125. C53 | #14341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810479 | 2 |
| #20272964 | 2 |
| #20272938 | 2 |
| C23×C22⋊C4×C53 | 2 |
| #14341 | 53 |