Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
4334 conjugacy classes of subgroups.
The subgroup lattice has 346 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C7 | C22⋊C4 |
| commutator | C22 | C22×C42×C7 |
| Frattini, cosocle | C24 | C24×C7 |
| prime radical | C26×C7 | C22 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C7 ◁ C26×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×C7×#342 | C2 | direct (N × H) |
| 6. C24×C4×C7 | C4 | semidirect |
| 11. C22×C7×C22⋊C4 | C4 | semidirect |
| 12. C22×C7×C22⋊C4 | C4 | semidirect |
| 15. C7×#342 | C22 | direct (N × H) |
| 16. C22×#342 | C7 | direct (N × H) |
| 32. C23×C4×C7 | C2×C4 | semidirect |
| 40. C2×C7×C22⋊C4 | C2×C4 | semidirect |
| 41. C2×C7×C22⋊C4 | C2×C4 | semidirect |
| 46. C2×#342 | C2×C7 | direct (N × H) |
| 84. C22×C4×C7 | C22×C4 | semidirect |
| 89. C7×C22⋊C4 | C22×C4 | semidirect |
| 92. C24×C4 | C4×C7 | semidirect |
| 97. C22×C22⋊C4 | C4×C7 | semidirect |
| 98. C22×C22⋊C4 | C4×C7 | semidirect |
| 101. #342 | C22×C7 | direct (N × H) |
| 164. C23×C4 | C2×C4×C7 | semidirect |
| 172. C2×C22⋊C4 | C2×C4×C7 | semidirect |
| 173. C2×C22⋊C4 | C2×C4×C7 | semidirect |
| 194. C22×C7 | #342 | direct (N × H) |
| 243. C22×C4 | C22×C4×C7 | semidirect |
| 248. C22⋊C4 | C22×C4×C7 | semidirect |
| 255. C2×C7 | C2×#342 | direct (N × H) |
| 305. C7 | C22×#342 | direct (N × H) |
| 324. C22 | C7×#342 | direct (N × H) |
| 342. C2 | C2×C7×#342 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C7×C22⋊C4 | 2 |
| C2×C7×#342 | 2 |
| C22×#342 | 7 |