Order 22784.
1710 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 |
|---|---|---|
| 21. C2×C4×Q8×C89 | C4 | semidirect |
| 32. C2×C4⋊Dic89 | Q8 | semidirect |
| 190. C89 | #13925 | semidirect |
| 194. 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×#19151464 | 2 |
| C2×C4×C4⋊Dic89 | 2 |
| #26018523 | 2 |
| #26018520 | 2 |
| #26018484 | 2 |
| #26018482 | 2 |
| C22×C4×Q8×C89 | 2 |
| #13925 | 89 |