Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
3246 conjugacy classes of subgroups.
The subgroup lattice has 356 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13071014 | C2 | direct (N × H) |
| 2. C2×#10622550 | C2 | semidirect |
| 3. C2×#10622549 | C2 | semidirect |
| 6. C2×C4×C4⋊Dic11 | C2 | semidirect |
| 8. C2×#10622545 | C2 | semidirect |
| 13. C22×C42×C11 | C4 | semidirect |
| 29. #10622550 | C22 | semidirect |
| 30. #10622549 | C22 | semidirect |
| 31. C4×C4⋊Dic11 | C22 | semidirect |
| 32. #10622545 | C22 | semidirect |
| 54. C2×C42×C11 | C2×C4 | semidirect |
| 167. C22×C42 | Dic11 | semidirect |
| 231. C2×C42 | C2×Dic11 | semidirect |
| 241. C2×C11 | #2283 | semidirect |
| 290. C11 | C2×#2283 | semidirect |
| 350. C2 | #13071014 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13071014 | 2 |
| C2×#10622550 | 2 |
| C2×#10622549 | 2 |
| C2×#10622824 | 2 |
| C2×#10622825 | 2 |
| C2×C4×C4⋊Dic11 | 2 |
| C2×C4×C22⋊Dic11 | 2 |
| C2×#10622545 | 2 |
| C23×C42×C11 | 2 |
| C2×#2283 | 11 |