Order 13568.
1702 conjugacy classes of subgroups.
The subgroup lattice has 348 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20283821 | C2 | semidirect |
| 2. #20283817 | C2 | semidirect |
| 3. #20283810 | C2 | semidirect |
| 4. Q8×#11719917 | C2 | semidirect |
| 8. #16810754 | C22 | semidirect |
| 9. #16810754 | C22 | semidirect |
| 10. Q8×#88322 | C22 | semidirect |
| 207. C53 | #60249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283821 | 2 |
| #20283817 | 2 |
| #20283810 | 2 |
| Q8×#11719917 | 2 |
| #20283353 | 2 |
| #20283348 | 2 |
| C2×C53×#533 | 2 |
| #60249 | 53 |