Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
2434 conjugacy classes of subgroups.
The subgroup lattice has 336 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #11739907 | C2 | semidirect |
| 4. Q8×C4⋊Dic7 | C2 | semidirect |
| 5. #11739896 | C2 | semidirect |
| 6. C4×Q8×Dic7 | C2 | semidirect |
| 11. C2×C4×C7×Q8 | C4 | semidirect |
| 62. #6489 | Q8 | direct (N × H) |
| 117. C4⋊Dic7 | C2×Q8 | semidirect |
| 121. C4×Dic7 | C2×Q8 | semidirect |
| 124. C2×C4×Q8 | Dic7 | semidirect |
| 156. C7×Q8 | #117 | semidirect |
| 162. C2×C4×C7 | C4×Q8 | semidirect |
| 286. Q8 | #6489 | direct (N × H) |
| 298. C2×C4 | Q8×Dic7 | semidirect |
| 310. C7 | Q8×#117 | 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 |
| Q8×C22⋊Dic7 | 2 |
| #11739907 | 2 |
| Q8×C4⋊Dic7 | 2 |
| #11739896 | 2 |
| C4×Q8×Dic7 | 2 |
| #11739605 | 2 |
| #11739507 | 2 |
| C4×#6489 | 2 |
| Q8×#117 | 7 |