Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1182 conjugacy classes of subgroups.
The subgroup lattice has 336 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 |
|---|---|---|
| 5. C7×#1942 | C2 | direct (N × H) |
| 14. C2×C7×#107 | C4 | semidirect |
| 23. C2×#1942 | C7 | direct (N × H) |
| 52. C7×#107 | C2×C4 | semidirect |
| 59. #1942 | C2×C7 | direct (N × H) |
| 89. C2×C7×C8 | C4⋊C4 | semidirect |
| 111. C2×#107 | C4×C7 | semidirect |
| 158. C7×C8 | C2×C4⋊C4 | semidirect |
| 187. #107 | C2×C4×C7 | semidirect |
| 241. C2×C8 | C7×C4⋊C4 | semidirect |
| 256. C2×C7 | #1942 | direct (N × H) |
| 302. C8 | C2×C7×C4⋊C4 | semidirect |
| 303. C7 | C2×#1942 | direct (N × H) |
| 327. C2 | C7×#1942 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×#107 | 2 |
| C22×C4×C7×C8 | 2 |
| C2×C7×#389 | 2 |
| C7×#1942 | 2 |
| C2×C7×#340 | 2 |
| C2×#1942 | 7 |