Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
946 conjugacy classes of subgroups.
The subgroup lattice has 466 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C22⋊C4 |
| commutator | C22 | C2×C4×C7×C8 |
| Frattini, cosocle | C23×C4 | C23×C7 |
| socle | C23×C7 | C2×C22⋊C4 |
| prime radical | C25×C7 | C2×C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ C22×C42×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×C7×C22⋊C8 | C2 | semidirect |
| 4. C7×#1280 | C2 | semidirect |
| 17. C7×#323 | C4 | direct (N × H) |
| 18. C4×#323 | C7 | direct (N × H) |
| 25. C23×C4×C7 | C8 | semidirect |
| 37. C2×C7×C22⋊C4 | C8 | semidirect |
| 46. C7×C22⋊C8 | C2×C4 | semidirect |
| 51. C4×C22⋊C8 | C2×C7 | semidirect |
| 53. #1280 | C2×C7 | semidirect |
| 126. #323 | C4×C7 | direct (N × H) |
| 153. C23×C7 | C4×C8 | semidirect |
| 203. C23×C4 | C7×C8 | semidirect |
| 215. C2×C22⋊C4 | C7×C8 | semidirect |
| 224. C22⋊C8 | C2×C4×C7 | semidirect |
| 268. C4×C7 | #323 | direct (N × H) |
| 367. C23 | C4×C7×C8 | semidirect |
| 411. C7 | C4×#323 | direct (N × H) |
| 452. C4 | C7×#323 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C7×C22⋊C4 | 2 |
| C4×C7×C22⋊C8 | 2 |
| C2×C7×#323 | 2 |
| C7×#1280 | 2 |
| C4×#323 | 7 |