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 |
|---|---|---|
| 1. C2×#16810661 | C2 | semidirect |
| 2. #20276920 | C2 | semidirect |
| 3. #20276903 | C2 | semidirect |
| 4. #20276504 | C2 | semidirect |
| 5. #20276427 | C2 | semidirect |
| 6. #20276326 | C2 | semidirect |
| 14. #16810450 | C22 | semidirect |
| 15. #16810448 | C22 | semidirect |
| 16. #16810427 | C22 | semidirect |
| 17. #16810424 | C22 | semidirect |
| 170. C53 | #33647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810661 | 2 |
| #20276920 | 2 |
| #20276903 | 2 |
| #20276504 | 2 |
| #20276427 | 2 |
| #20276326 | 2 |
| C53×#3050 | 2 |
| #33647 | 53 |