Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1974 conjugacy classes of subgroups.
The subgroup lattice has 314 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11739882 | C2 | semidirect |
| 3. #11739881 | C2 | semidirect |
| 4. #11739880 | C2 | semidirect |
| 5. Q8×#1136 | C2 | semidirect |
| 19. #89796 | C22 | semidirect |
| 20. Q8×C7⋊C8 | C22 | semidirect |
| 74. C2×C7×Q8 | M16 | semidirect |
| 217. C2×Q8 | #1136 | semidirect |
| 287. C7 | #60248 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C7×Q8 | 2 |
| #11739882 | 2 |
| #11739881 | 2 |
| #11739880 | 2 |
| Q8×#1136 | 2 |
| #11739494 | 2 |
| #60248 | 7 |