Order 22784.
2614 conjugacy classes of subgroups.
The subgroup lattice has 364 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #26025614 | C2 | direct (N × H) |
| 60. C22×Q8×C89 | Q8 | semidirect |
| 99. C2×Q8×C89 | C2×Q8 | semidirect |
| 176. C2×C89 | #2581 | semidirect |
| 191. C89 | C2×#2581 | semidirect |
| 223. C22×Q8 | Dic178 | semidirect |
| 265. C2×Q8 | C2×Dic178 | semidirect |
| 357. C2 | #26025614 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×Dic178 | 2 |
| #26025614 | 2 |
| C2×#19151537 | 2 |
| C2×#19151518 | 2 |
| C2×#19151505 | 2 |
| C2×#19151494 | 2 |
| C2×#19151482 | 2 |
| C2×#19151464 | 2 |
| C22×C4×Q8×C89 | 2 |
| C2×#2581 | 89 |