Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
3086 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 |
|---|---|---|
| 3. C2×#89697 | C2 | direct (N × H) |
| 4. C22×C4⋊(C7⋊C8) | C2 | semidirect |
| 5. C22×C4×C7⋊C8 | C2 | semidirect |
| 17. #89697 | C22 | direct (N × H) |
| 18. C2×C4⋊(C7⋊C8) | C22 | semidirect |
| 19. C2×C4×C7⋊C8 | C22 | semidirect |
| 24. C23×C4×C7 | C8 | semidirect |
| 46. C4⋊(C7⋊C8) | C23 | semidirect |
| 47. C4×C7⋊C8 | C23 | semidirect |
| 65. C22×C4×C7 | C2×C8 | semidirect |
| 118. C2×C4×C7 | C22×C8 | semidirect |
| 132. C23×C4 | C7⋊C8 | semidirect |
| 159. C22×C7 | #431 | semidirect |
| 184. C22×C4 | C2×C7⋊C8 | semidirect |
| 207. C2×C7 | C2×#431 | semidirect |
| 227. C2×C4 | C22×C7⋊C8 | semidirect |
| 239. C7 | C22×#431 | semidirect |
| 243. C22 | #89697 | direct (N × H) |
| 257. C2 | C2×#89697 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C42×C7 | 2 |
| C22×C22⋊(C7⋊C8) | 2 |
| C2×#89697 | 2 |
| C22×C4⋊(C7⋊C8) | 2 |
| C22×C4×C7⋊C8 | 2 |
| C22×#431 | 7 |