Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
450 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 90 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×#16811542 | C2 | semidirect |
| 3. #20291025 | C2 | semidirect |
| 5. #20289795 | C2 | semidirect |
| 6. #20289784 | C2 | semidirect |
| 25. #16810899 | C4 | semidirect |
| 26. #16810898 | C4 | semidirect |
| 29. #16810895 | C4 | semidirect |
| 32. C53×#473 | C4 | semidirect |
| 239. #473 | #6157 | semidirect |
| 249. C53 | #13069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291683 | 2 |
| C2×#16811542 | 2 |
| #20291025 | 2 |
| #20290601 | 2 |
| #20289795 | 2 |
| #20289784 | 2 |
| #473×D53 | 2 |
| #13069 | 53 |