Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
3006 conjugacy classes of subgroups.
The subgroup lattice has 270 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #13071537 | C2 | semidirect |
| 3. #13071526 | C2 | semidirect |
| 4. #13071239 | C2 | semidirect |
| 5. #13071023 | C2 | semidirect |
| 6. C2×#10622549 | C2 | semidirect |
| 9. C4×C11×#41 | C4 | semidirect |
| 37. C4×Q8×C11 | C2×C4 | semidirect |
| 38. C4×D4×C11 | C2×C4 | semidirect |
| 39. C11×#117 | C2×C4 | semidirect |
| 42. C2×C42×C11 | C2×C4 | semidirect |
| 61. C11×#41 | C4⋊C4 | semidirect |
| 125. C4×#41 | Dic11 | semidirect |
| 167. C4×Q8 | C2×Dic11 | semidirect |
| 169. C4×D4 | C2×Dic11 | semidirect |
| 171. #117 | C2×Dic11 | semidirect |
| 181. C2×C42 | C2×Dic11 | semidirect |
| 194. #41 | C4⋊Dic11 | semidirect |
| 225. C11 | #34184 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10623358 | 2 |
| #13071537 | 2 |
| #13071526 | 2 |
| #13071239 | 2 |
| #13071023 | 2 |
| C2×#10622549 | 2 |
| C2×C4×C11×#41 | 2 |
| #34184 | 11 |