Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
2830 conjugacy classes of subgroups.
The subgroup lattice has 280 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C24 |
| commutator | C22 | C24×C4×C7 |
| Frattini, cosocle | C2×C4 | C25×C7 |
| socle | C23×C7 | C23×C4 |
| prime radical | C25×C7 | C2×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C7×#2905 | C2 | direct (N × H) |
| 4. C2×C7×#424 | C2 | semidirect |
| 5. C2×C7×#423 | C2 | semidirect |
| 19. C7×#424 | C22 | semidirect |
| 20. C7×#423 | C22 | semidirect |
| 21. C2×C7×C4⋊C8 | C22 | semidirect |
| 22. C2×#2905 | C7 | direct (N × H) |
| 52. C7×C4⋊C8 | C23 | semidirect |
| 55. #2905 | C2×C7 | direct (N × H) |
| 56. C2×#424 | C2×C7 | semidirect |
| 57. C2×#423 | C2×C7 | semidirect |
| 107. #424 | C22×C7 | semidirect |
| 108. #423 | C22×C7 | semidirect |
| 109. C2×C4⋊C8 | C22×C7 | semidirect |
| 169. C4⋊C8 | C23×C7 | semidirect |
| 224. C2×C7 | #2905 | direct (N × H) |
| 257. C7 | C2×#2905 | direct (N × H) |
| 276. C2 | C7×#2905 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C7×M16 | 2 |
| C22×C7×#117 | 2 |
| C7×#2905 | 2 |
| C2×C7×#424 | 2 |
| C2×C7×#423 | 2 |
| C2×#2905 | 7 |