Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
2830 conjugacy classes of subgroups.
The subgroup lattice has 280 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #13077180 | C2 | direct (N × H) |
| 3. C2×#10622612 | C2 | semidirect |
| 4. C2×#10622537 | C2 | semidirect |
| 19. #10622612 | C22 | semidirect |
| 20. #10622537 | C22 | semidirect |
| 21. C2×C4⋊(C11⋊C8) | C22 | semidirect |
| 51. C4⋊(C11⋊C8) | C23 | semidirect |
| 188. C2×C11 | #2905 | semidirect |
| 227. C11 | C2×#2905 | semidirect |
| 276. C2 | #13077180 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#4318 | 2 |
| #13077180 | 2 |
| C2×#10622612 | 2 |
| C2×#10622537 | 2 |
| C22×C11×#117 | 2 |
| C2×#2905 | 11 |