Order 22784.
1154 conjugacy classes of subgroups.
The subgroup lattice has 346 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#15667952 | C2 | semidirect |
| 2. #26021873 | C2 | direct (N × H) |
| 3. C2×#19151380 | C2 | semidirect |
| 8. C2×#15667952 | C22 | semidirect |
| 10. #19151380 | C22 | semidirect |
| 171. C2×C89 | #2115 | semidirect |
| 177. C89 | C2×#2115 | semidirect |
| 343. C2 | #26021873 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667952 | 2 |
| #26021873 | 2 |
| C2×#19151380 | 2 |
| C22×#131×C89 | 2 |
| C2×#2115 | 89 |