Order 22784.
1342 conjugacy classes of subgroups.
The subgroup lattice has 388 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 24. #376×C89 | C4 | semidirect |
| 107. C42×C89 | C4⋊C4 | semidirect |
| 202. C89 | #13952 | semidirect |
| 210. #376 | Dic89 | semidirect |
| 301. C42 | C4⋊Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151466 | 2 |
| C2×C4×C4⋊Dic89 | 2 |
| #26018517 | 2 |
| #26018509 | 2 |
| #26018486 | 2 |
| #26018482 | 2 |
| #26018479 | 2 |
| C2×#376×C89 | 2 |
| #13952 | 89 |