Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
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 |
|---|---|---|
| 2. #11740775 | C2 | semidirect |
| 3. #11740773 | C2 | semidirect |
| 6. Q8×#1136 | C2 | semidirect |
| 7. C2×Q8×C7⋊C8 | C2 | semidirect |
| 52. #6511 | Q8 | direct (N × H) |
| 96. #1136 | C2×Q8 | semidirect |
| 98. C2×C7⋊C8 | C2×Q8 | semidirect |
| 130. C7×Q8 | #131 | semidirect |
| 229. Q8 | #6511 | direct (N × H) |
| 245. C7 | Q8×#131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×Q8×#41 | 2 |
| #11740775 | 2 |
| #11740773 | 2 |
| #11739957 | 2 |
| C4×#6511 | 2 |
| Q8×#1136 | 2 |
| C2×Q8×C7⋊C8 | 2 |
| Q8×#131 | 7 |