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×#10622541 | C2 | direct (N × H) |
| 15. C22×C4⋊Dic11 | C4 | semidirect |
| 21. #10622541 | C22 | direct (N × H) |
| 46. C2×C4⋊Dic11 | C2×C4 | semidirect |
| 67. C22×C4×C11 | C4⋊C4 | semidirect |
| 88. C4⋊Dic11 | C22×C4 | semidirect |
| 117. C2×C4×C11 | C2×C4⋊C4 | semidirect |
| 146. C22×C11 | #389 | semidirect |
| 163. C4×C11 | C22×C4⋊C4 | semidirect |
| 196. C2×C11 | C2×#389 | semidirect |
| 228. C22×C4 | Dic11⋊C4 | semidirect |
| 241. C11 | C22×#389 | semidirect |
| 271. C2×C4 | C2×Dic11⋊C4 | semidirect |
| 277. C22 | #10622541 | direct (N × H) |
| 296. C4 | C22×Dic11⋊C4 | semidirect |
| 297. C2 | C2×#10622541 | 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×Dic11⋊C4 | 2 |
| C2×#10622541 | 2 |
| C22×C11⋊#95 | 2 |
| C23×C42×C11 | 2 |
| C22×#389 | 11 |