Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
2350 conjugacy classes of subgroups.
The subgroup lattice has 402 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C22⋊C4 |
| commutator | C22 | C22×C42×C7 |
| Frattini, cosocle | C24 | C24×C7 |
| socle | C23×C7 | C2×C22⋊C4 |
| prime radical | C25×C7 | C23 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ C24×C4×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C7×#1740 | C2 | direct (N × H) |
| 11. C2×C7×#117 | C4 | semidirect |
| 12. C2×C7×#117 | C4 | semidirect |
| 16. C22×C7×C4⋊C4 | C4 | semidirect |
| 20. C22×C42×C7 | C4 | semidirect |
| 22. C2×#1740 | C7 | direct (N × H) |
| 42. C7×#117 | C2×C4 | semidirect |
| 47. C2×C7×C4⋊C4 | C2×C4 | semidirect |
| 61. C2×C42×C7 | C2×C4 | semidirect |
| 64. #1740 | C2×C7 | direct (N × H) |
| 124. C2×#117 | C4×C7 | semidirect |
| 125. C2×#117 | C4×C7 | semidirect |
| 129. C22×C4⋊C4 | C4×C7 | semidirect |
| 133. C22×C42 | C4×C7 | semidirect |
| 203. #117 | C2×C4×C7 | semidirect |
| 208. C2×C4⋊C4 | C2×C4×C7 | semidirect |
| 222. C2×C42 | C2×C4×C7 | semidirect |
| 310. C2×C7 | #1740 | direct (N × H) |
| 362. C7 | C2×#1740 | direct (N × H) |
| 398. C2 | C7×#1740 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×#117 | 2 |
| C7×#1740 | 2 |
| C2×C7×#342 | 2 |
| C2×#1740 | 7 |