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. #20276923 | C2 | semidirect |
| 3. #20276906 | C2 | semidirect |
| 4. #20276501 | C2 | semidirect |
| 5. #20276425 | C2 | semidirect |
| 6. #20276326 | C2 | semidirect |
| 7. C2×C53×#427 | C2 | semidirect |
| 16. #16810450 | C22 | semidirect |
| 17. #16810448 | C22 | semidirect |
| 18. #16810426 | C22 | semidirect |
| 19. #16810423 | C22 | semidirect |
| 140. C2×#427 | 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 |
| #20276923 | 2 |
| #20276906 | 2 |
| #20276501 | 2 |
| #20276425 | 2 |
| #20276326 | 2 |
| C2×C53×#427 | 2 |
| #33647 | 53 |