Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
3278 conjugacy classes of subgroups.
The subgroup lattice has 238 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #13077044 | C2 | direct (N × H) |
| 3. C2×#10622610 | C2 | semidirect |
| 4. C2×C4×#4318 | C2 | semidirect |
| 5. C22×#66867 | C2 | semidirect |
| 14. C2×#67001 | C4 | semidirect |
| 18. #10622610 | C22 | semidirect |
| 19. C4×#4318 | C22 | semidirect |
| 23. C2×#66867 | C22 | semidirect |
| 43. #67001 | C2×C4 | semidirect |
| 44. C2×#4318 | C2×C4 | semidirect |
| 46. C22×C11⋊C8 | C2×C4 | semidirect |
| 78. #4318 | C22×C4 | semidirect |
| 81. C2×C11⋊C8 | C22×C4 | semidirect |
| 169. C2×C11 | #2875 | semidirect |
| 201. C11 | C2×#2875 | semidirect |
| 234. C2 | #13077044 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#67001 | 2 |
| #13077044 | 2 |
| C2×#10622610 | 2 |
| C2×C4×#4318 | 2 |
| C22×#66867 | 2 |
| C2×C4×C11×#41 | 2 |
| C2×#2875 | 11 |