Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
936 conjugacy classes of subgroups.
The subgroup lattice has 426 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#89320 | C2 | semidirect |
| 3. #11729284 | C2 | semidirect |
| 4. C4×C22⋊(C7⋊C8) | C2 | semidirect |
| 28. C22×C7×D4 | C8 | semidirect |
| 52. C22⋊(C7⋊C8) | D4 | semidirect |
| 195. C22×D4 | C7⋊C8 | semidirect |
| 255. C4×C7 | #323 | semidirect |
| 380. C7 | #9649 | semidirect |
| 414. C4 | #89320 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#390 | 2 |
| C2×#89320 | 2 |
| #11729284 | 2 |
| C4×C22⋊(C7⋊C8) | 2 |
| #9649 | 7 |