Order 22784.
2574 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. #26025640 | C2 | direct (N × H) |
| 42. C2×C4⋊Dic89 | Q8 | semidirect |
| 89. C4⋊Dic89 | C2×Q8 | semidirect |
| 176. C2×C89 | #2584 | semidirect |
| 191. C89 | C2×#2584 | semidirect |
| 357. C2 | #26025640 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668004 | 2 |
| #26025640 | 2 |
| C2×#19151529 | 2 |
| C2×#19151517 | 2 |
| C2×#19151496 | 2 |
| C2×#19151493 | 2 |
| C2×C4×C4⋊Dic89 | 2 |
| C22×C4×Q8×C89 | 2 |
| C2×#2584 | 89 |