Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
584 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×#16810661 | C2 | semidirect |
| 3. #20276924 | C2 | semidirect |
| 4. #20276907 | C2 | semidirect |
| 5. #20276503 | C2 | semidirect |
| 6. #20276428 | C2 | semidirect |
| 7. C53×#2112 | C2 | semidirect |
| 20. #16810451 | C22 | semidirect |
| 21. #16810449 | C22 | semidirect |
| 22. #16810428 | C22 | semidirect |
| 23. #16810425 | C22 | semidirect |
| 145. #2112 | D53 | semidirect |
| 170. C53 | #33647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284296 | 2 |
| C2×#16810661 | 2 |
| #20276924 | 2 |
| #20276907 | 2 |
| #20276503 | 2 |
| #20276428 | 2 |
| C53×#2112 | 2 |
| #33647 | 53 |