Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
2810 conjugacy classes of subgroups.
The subgroup lattice has 298 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #13077184 | C2 | direct (N × H) |
| 3. C2×#10622612 | C2 | semidirect |
| 4. C2×#10622537 | C2 | semidirect |
| 5. C22×C4⋊(C11⋊C8) | C2 | semidirect |
| 20. #10622612 | C22 | semidirect |
| 21. #10622537 | C22 | semidirect |
| 26. C2×C4⋊(C11⋊C8) | C22 | semidirect |
| 120. C2×C4×C11 | #131 | semidirect |
| 167. C4×C11 | C2×#131 | semidirect |
| 206. C2×C11 | #2906 | semidirect |
| 247. C11 | C2×#2906 | semidirect |
| 262. C2×C4 | #67001 | semidirect |
| 289. C4 | C2×#67001 | semidirect |
| 293. C2 | #13077184 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#67001 | 2 |
| #13077184 | 2 |
| C2×#10622612 | 2 |
| C2×#10622537 | 2 |
| C22×C4⋊(C11⋊C8) | 2 |
| C2×C4×C11×#41 | 2 |
| C2×#2906 | 11 |