Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
4894 conjugacy classes of subgroups.
The subgroup lattice has 306 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C2×#10622598 | C2 | direct (N × H) |
| 12. C22×C11×C4⋊C4 | C4 | semidirect |
| 21. #10622598 | C22 | direct (N × H) |
| 43. C2×C11×C4⋊C4 | C2×C4 | semidirect |
| 64. C22×C4×C11 | C4⋊C4 | semidirect |
| 86. C11×C4⋊C4 | C22×C4 | semidirect |
| 114. C2×C4×C11 | C2×C4⋊C4 | semidirect |
| 140. C22×C4⋊C4 | Dic11 | semidirect |
| 146. C22×C11 | #389 | semidirect |
| 162. C4×C11 | C22×C4⋊C4 | semidirect |
| 191. C2×C4⋊C4 | C2×Dic11 | semidirect |
| 196. C2×C11 | C2×#389 | semidirect |
| 230. C22×C4 | C4⋊Dic11 | semidirect |
| 239. C4⋊C4 | C22×Dic11 | semidirect |
| 241. C11 | C22×#389 | semidirect |
| 272. C2×C4 | C2×C4⋊Dic11 | semidirect |
| 277. C22 | #10622598 | direct (N × H) |
| 296. C4 | C22×C4⋊Dic11 | semidirect |
| 297. C2 | C2×#10622598 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4⋊Dic11 | 2 |
| C23×C4×Dic11 | 2 |
| C2×#10622598 | 2 |
| C22×C11⋊#95 | 2 |
| C23×C11×C4⋊C4 | 2 |
| C22×#389 | 11 |