Order 13568.
650 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. #20272579 | C2 | semidirect |
| 8. #16810680 | C4 | semidirect |
| 14. C4×#11719917 | C4 | semidirect |
| 17. C2×#13133128 | C4 | semidirect |
| 18. C2×C4×#88322 | C4 | semidirect |
| 210. C53 | #7972 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810680 | 2 |
| C2×C4×#11719917 | 2 |
| #20272579 | 2 |
| C53×#2283 | 2 |
| #7972 | 53 |