Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
782 conjugacy classes of subgroups.
The subgroup lattice has 422 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #11725497 | C2 | direct (N × H) |
| 5. C22×C7×M16 | C4 | semidirect |
| 6. C23×C7×C8 | C4 | semidirect |
| 9. C7×#408 | C4 | semidirect |
| 14. #90012 | C4 | semidirect |
| 17. C2×#6408 | C4 | semidirect |
| 37. C2×C7×M16 | C2×C4 | semidirect |
| 43. C22×C7×C8 | C2×C4 | semidirect |
| 56. #6408 | C2×C4 | semidirect |
| 127. C22×M16 | Dic7 | semidirect |
| 128. C23×C8 | Dic7 | semidirect |
| 137. #408 | Dic7 | semidirect |
| 213. C2×M16 | C2×Dic7 | semidirect |
| 219. C22×C8 | C2×Dic7 | semidirect |
| 330. C2×C7 | #1391 | semidirect |
| 387. C7 | C2×#1391 | semidirect |
| 419. C2 | #11725497 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#408 | 2 |
| C2×#90012 | 2 |
| #11725497 | 2 |
| C2×#1391 | 7 |