Order 22784.
1554 conjugacy classes of subgroups.
The subgroup lattice has 370 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #26020360 | C2 | direct (N × H) |
| 3. C2×#19151364 | C2 | semidirect |
| 9. #19151364 | C22 | semidirect |
| 12. #518×C89 | C4 | semidirect |
| 15. C2×#117×C89 | C4 | semidirect |
| 16. C22×C22⋊C4×C89 | C4 | semidirect |
| 40. #117×C89 | C2×C4 | semidirect |
| 49. C2×C22⋊C4×C89 | C2×C4 | semidirect |
| 183. C2×C89 | #1828 | semidirect |
| 189. C89 | C2×#1828 | semidirect |
| 192. #518 | Dic89 | semidirect |
| 195. C2×#117 | Dic89 | semidirect |
| 197. C22×C22⋊C4 | Dic89 | semidirect |
| 218. #117 | C2×Dic89 | semidirect |
| 233. C2×C22⋊C4 | C2×Dic89 | semidirect |
| 367. C2 | #26020360 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667927 | 2 |
| #26020360 | 2 |
| C2×#19151364 | 2 |
| C2×#518×C89 | 2 |
| C2×#1828 | 89 |