Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
1974 conjugacy classes of subgroups.
The subgroup lattice has 314 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13077705 | C2 | semidirect |
| 2. #13077701 | C2 | semidirect |
| 3. #13077697 | C2 | semidirect |
| 4. Q8×#4318 | C2 | semidirect |
| 19. #10622637 | C22 | semidirect |
| 20. Q8×C11⋊C8 | C22 | semidirect |
| 68. C2×Q8×C11 | M16 | semidirect |
| 223. C2×Q8 | #4318 | semidirect |
| 256. C11 | #60248 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13077705 | 2 |
| #13077701 | 2 |
| #13077697 | 2 |
| Q8×#4318 | 2 |
| #13077249 | 2 |
| C22×C4×Q8×C11 | 2 |
| #60248 | 11 |