Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1978 conjugacy classes of subgroups.
The subgroup lattice has 260 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C24 |
| commutator | C22 | C24×C4×C7 |
| Frattini, cosocle | C2×C4 | C25×C7 |
| socle | C23×C7 | C23×C4 |
| prime radical | C24×C7 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C7×#2983 | C2 | direct (N × H) |
| 3. C2×C7×#446 | C2 | semidirect |
| 15. C7×#446 | C22 | semidirect |
| 23. C2×#2983 | C7 | direct (N × H) |
| 54. #2983 | C2×C7 | direct (N × H) |
| 55. C2×#446 | C2×C7 | semidirect |
| 98. #446 | C22×C7 | semidirect |
| 208. C2×C7 | #2983 | direct (N × H) |
| 238. C7 | C2×#2983 | direct (N × H) |
| 255. C2 | C7×#2983 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C7×Q8 | 2 |
| C7×#2983 | 2 |
| C2×C7×#446 | 2 |
| C2×C7×#432 | 2 |
| C2×C7×#431 | 2 |
| C2×#2983 | 7 |