Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2122 conjugacy classes of subgroups.
The subgroup lattice has 360 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20283381 | C2 | semidirect |
| 2. #20283353 | C2 | semidirect |
| 3. #20283348 | C2 | semidirect |
| 4. C2×#16810647 | C2 | semidirect |
| 6. #20283134 | C2 | semidirect |
| 9. #16810684 | C22 | semidirect |
| 10. #16810680 | C22 | semidirect |
| 11. #16810676 | C22 | semidirect |
| 14. #16810647 | C22 | semidirect |
| 15. C2×C4⋊#88322 | C22 | semidirect |
| 18. #16810579 | C22 | semidirect |
| 210. C53 | #60125 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283381 | 2 |
| #20283353 | 2 |
| #20283348 | 2 |
| C2×#16810647 | 2 |
| #20283160 | 2 |
| #20283134 | 2 |
| C2×C4×#41×C53 | 2 |
| #60125 | 53 |