Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
3086 conjugacy classes of subgroups.
The subgroup lattice has 262 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10622538 | C2 | direct (N × H) |
| 2. C22×C4⋊(C11⋊C8) | C2 | semidirect |
| 4. C22×C4×C11⋊C8 | C2 | semidirect |
| 17. #10622538 | C22 | direct (N × H) |
| 18. C2×C4⋊(C11⋊C8) | C22 | semidirect |
| 19. C2×C4×C11⋊C8 | C22 | semidirect |
| 23. C23×C4×C11 | C8 | semidirect |
| 45. C4⋊(C11⋊C8) | C23 | semidirect |
| 46. C4×C11⋊C8 | C23 | semidirect |
| 60. C22×C4×C11 | C2×C8 | semidirect |
| 104. C2×C4×C11 | C22×C8 | semidirect |
| 132. C22×C11 | #431 | semidirect |
| 148. C23×C4 | C11⋊C8 | semidirect |
| 173. C2×C11 | C2×#431 | semidirect |
| 189. C22×C4 | C2×C11⋊C8 | semidirect |
| 211. C11 | C22×#431 | semidirect |
| 228. C2×C4 | C22×C11⋊C8 | semidirect |
| 243. C22 | #10622538 | direct (N × H) |
| 257. C2 | C2×#10622538 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622538 | 2 |
| C22×C4⋊(C11⋊C8) | 2 |
| C22×C22⋊(C11⋊C8) | 2 |
| C22×C4×C11⋊C8 | 2 |
| C23×C42×C11 | 2 |
| C22×#431 | 11 |