Order 22784.
1306 conjugacy classes of subgroups.
The subgroup lattice has 366 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #26020267 | C2 | semidirect |
| 6. #26020082 | C2 | semidirect |
| 25. C2×C4×Q8×C89 | C4 | semidirect |
| 190. C89 | #20741 | semidirect |
| 195. C2×C4×Q8 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151655 | 2 |
| #26022650 | 2 |
| #26020342 | 2 |
| #26020267 | 2 |
| #26020187 | 2 |
| #26020082 | 2 |
| C22×C4×Q8×C89 | 2 |
| #20741 | 89 |