Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
456 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 98 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. #20290470 | C2 | semidirect |
| 3. #20289806 | C2 | semidirect |
| 4. #20289803 | C2 | semidirect |
| 9. #16811525 | C4 | semidirect |
| 10. #16811523 | C4 | semidirect |
| 16. #16810649 | C4 | semidirect |
| 18. #16810587 | C4 | semidirect |
| 19. #16810578 | C4 | semidirect |
| 20. C22×M16×C53 | C4 | semidirect |
| 149. C22×M16 | #6157 | semidirect |
| 163. C53 | #12624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290966 | 2 |
| #20290470 | 2 |
| #20289806 | 2 |
| #20289803 | 2 |
| #20283418 | 2 |
| #12624 | 53 |