Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
3854 conjugacy classes of subgroups.
The subgroup lattice has 324 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #13071100 | C2 | direct (N × H) |
| 4. C2×#10622598 | C2 | semidirect |
| 6. C2×C4×C4⋊Dic11 | C2 | semidirect |
| 10. C2×C11×#117 | C4 | semidirect |
| 26. #10622598 | C22 | semidirect |
| 28. C4×C4⋊Dic11 | C22 | semidirect |
| 42. C11×#117 | C2×C4 | semidirect |
| 43. C2×C11×C4⋊C4 | C2×C4 | semidirect |
| 47. C2×C42×C11 | C2×C4 | semidirect |
| 72. C22×C4×C11 | C4⋊C4 | semidirect |
| 96. C11×C4⋊C4 | C22×C4 | semidirect |
| 98. C42×C11 | C22×C4 | semidirect |
| 129. C2×C4×C11 | C2×C4⋊C4 | semidirect |
| 149. C2×#117 | Dic11 | semidirect |
| 198. #117 | C2×Dic11 | semidirect |
| 203. C2×C4⋊C4 | C2×Dic11 | semidirect |
| 216. C2×C42 | C2×Dic11 | semidirect |
| 220. C2×C11 | #2296 | semidirect |
| 242. C22×C4 | C4⋊Dic11 | semidirect |
| 258. C4⋊C4 | C22×Dic11 | semidirect |
| 264. C42 | C22×Dic11 | semidirect |
| 265. C11 | C2×#2296 | semidirect |
| 291. C2×C4 | C2×C4⋊Dic11 | semidirect |
| 318. C2 | #13071100 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#66979 | 2 |
| C23×C4×Dic11 | 2 |
| #13071100 | 2 |
| C2×#10622598 | 2 |
| C2×#10622563 | 2 |
| C2×C4×C4⋊Dic11 | 2 |
| C22×C11×#117 | 2 |
| C2×#2296 | 11 |