Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
4818 conjugacy classes of subgroups.
The subgroup lattice has 268 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C22×C22⋊C4 |
| commutator | C22 | C24×C4×C7 |
| Frattini, cosocle | C23 | C25×C7 |
| prime radical | C22×C7×2−1+4 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C7×Q8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C7×#519 | C2 | semidirect |
| 3. C7×#2884 | C2 | direct (N × H) |
| 4. C2×C7×#410 | C2 | semidirect |
| 7. C2×C7×2−1+4 | C4 | semidirect |
| 9. C22×C7×#41 | C4 | semidirect |
| 11. C23×C7×Q8 | C4 | semidirect |
| 14. C7×#519 | C22 | semidirect |
| 17. C7×#410 | C22 | semidirect |
| 19. C2×#2884 | C7 | direct (N × H) |
| 27. C2×C7×#41 | C2×C4 | semidirect |
| 34. C22×C7×Q8 | C2×C4 | semidirect |
| 50. C2×#519 | C2×C7 | semidirect |
| 51. #2884 | C2×C7 | direct (N × H) |
| 52. C2×#410 | C2×C7 | semidirect |
| 90. C2×2−1+4 | C4×C7 | semidirect |
| 92. C22×#41 | C4×C7 | semidirect |
| 94. C23×Q8 | C4×C7 | semidirect |
| 97. #519 | C22×C7 | semidirect |
| 100. #410 | C22×C7 | semidirect |
| 135. C2×#41 | C2×C4×C7 | semidirect |
| 142. C22×Q8 | C2×C4×C7 | semidirect |
| 214. C2×C7 | #2884 | direct (N × H) |
| 242. C7 | C2×#2884 | direct (N × H) |
| 265. C2 | C7×#2884 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×2−1+4 | 2 |
| C2×C7×#519 | 2 |
| C7×#2884 | 2 |
| C2×C7×#410 | 2 |
| C2×#2884 | 7 |