Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1154 conjugacy classes of subgroups; only the 391 normal subgroups are shown.
This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 391 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. #20287818 | C2 | semidirect |
| 2. #20283326 | C2 | semidirect |
| 3. #20276464 | C2 | semidirect |
| 4. C2×#16810436 | C2 | semidirect |
| 8. C2×#13133157 | C22 | semidirect |
| 10. C2×#13133153 | C22 | semidirect |
| 11. #16810439 | C22 | semidirect |
| 12. #16810436 | C22 | semidirect |
| 135. C53 | #33392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287818 | 2 |
| #20283326 | 2 |
| #20276464 | 2 |
| C2×#16810436 | 2 |
| C2×C53×#576 | 2 |
| #33392 | 53 |