Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1550 conjugacy classes of subgroups.
The subgroup lattice has 328 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C7 | C2×D4 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C7 ◁ C22×C42×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C7×#1990 | C2 | direct (N × H) |
| 10. C2×C7×C4⋊Q8 | C4 | semidirect |
| 23. C2×#1990 | C7 | direct (N × H) |
| 35. C22×C7×C8 | Q8 | semidirect |
| 39. C7×C4⋊Q8 | C2×C4 | semidirect |
| 61. #1990 | C2×C7 | direct (N × H) |
| 93. C2×C7×C8 | C2×Q8 | semidirect |
| 109. C2×C4⋊Q8 | C4×C7 | semidirect |
| 168. C22×C8 | C7×Q8 | semidirect |
| 172. C4⋊Q8 | C2×C4×C7 | semidirect |
| 242. C2×C8 | C2×C7×Q8 | semidirect |
| 254. C2×C7 | #1990 | direct (N × H) |
| 297. C7 | C2×#1990 | direct (N × H) |
| 319. C2 | C7×#1990 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×C4⋊Q8 | 2 |
| C22×C4×C7×C8 | 2 |
| C2×C7×#384 | 2 |
| C7×#1990 | 2 |
| C2×C7×#340 | 2 |
| C2×#1990 | 7 |