Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
1882 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. Q8×#4318 | C2 | semidirect |
| 2. #13077565 | C2 | semidirect |
| 3. #13077551 | C2 | semidirect |
| 4. C2×Q8×C11⋊C8 | C2 | semidirect |
| 51. #67001 | Q8 | direct (N × H) |
| 89. #4318 | C2×Q8 | semidirect |
| 91. C2×C11⋊C8 | C2×Q8 | semidirect |
| 107. Q8×C11 | #131 | semidirect |
| 225. C11 | Q8×#131 | semidirect |
| 230. Q8 | #67001 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#4318 | 2 |
| #13077565 | 2 |
| #13077551 | 2 |
| C2×Q8×C11⋊C8 | 2 |
| #13077184 | 2 |
| C4×#67001 | 2 |
| Q8×C11×#41 | 2 |
| Q8×#131 | 11 |