Order 22784.
1334 conjugacy classes of subgroups.
The subgroup lattice has 384 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #26021605 | C2 | semidirect |
| 42. C2×C22⋊Dic89 | Q8 | semidirect |
| 60. C2×C22⋊C4×C89 | Q8 | semidirect |
| 82. C22⋊Dic89 | C2×Q8 | semidirect |
| 110. C22⋊C4×C89 | C2×Q8 | semidirect |
| 198. C89 | #23565 | semidirect |
| 250. C2×C22⋊C4 | Dic178 | semidirect |
| 302. C22⋊C4 | C2×Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152224 | 2 |
| #26022864 | 2 |
| #26021605 | 2 |
| C2×#19151365 | 2 |
| C2×#19151364 | 2 |
| C89×#2315 | 2 |
| #23565 | 89 |