Order 13568.
684 conjugacy classes of subgroups.
The subgroup lattice has 368 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #20272548 | C2 | semidirect |
| 6. #16810680 | C4 | semidirect |
| 10. #16810676 | C4 | semidirect |
| 13. #16810647 | C4 | semidirect |
| 14. C2×C4⋊#88322 | C4 | semidirect |
| 210. C53 | #7870 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283348 | 2 |
| C2×#16810676 | 2 |
| #20272548 | 2 |
| C4×#117×C53 | 2 |
| #7870 | 53 |