Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1810 conjugacy classes of subgroups.
The subgroup lattice has 170 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C2×C7×C8 | C24 |
| commutator | C22 | C24×C4×C7 |
| Frattini, cosocle | C2×C4 | C25×C7 |
| socle | C22×C7 | C24×C4 |
| prime radical | C24×C7 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C7×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C7×#2961 | C2 | semidirect |
| 3. C7×#2960 | C2 | semidirect |
| 12. C7×#446 | C22 | semidirect |
| 13. C7×C8×Q8 | C22 | semidirect |
| 20. #60191 | C7 | direct (N × H) |
| 24. C22×C7×C8 | Q8 | semidirect |
| 42. #2961 | C2×C7 | semidirect |
| 43. #2960 | C2×C7 | semidirect |
| 71. #446 | C22×C7 | semidirect |
| 72. C8×Q8 | C22×C7 | semidirect |
| 96. C22×C8 | C7×Q8 | semidirect |
| 157. C7 | #60191 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3458 | 2 |
| C7×#2961 | 2 |
| C7×#2960 | 2 |
| C7×#2905 | 2 |
| C2×C7×#405 | 2 |
| #60191 | 7 |