Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1746 conjugacy classes of subgroups.
The subgroup lattice has 398 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C4×C7×Q8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C7×#3390 | C2 | direct (N × H) |
| 46. C2×#3390 | C7 | direct (N × H) |
| 50. C2×C7×Q16 | Q8 | semidirect |
| 105. #3390 | C2×C7 | direct (N × H) |
| 131. C7×Q16 | C2×Q8 | semidirect |
| 228. C2×Q16 | C7×Q8 | semidirect |
| 314. Q16 | C2×C7×Q8 | semidirect |
| 344. C2×C7 | #3390 | direct (N × H) |
| 377. C7 | C2×#3390 | direct (N × H) |
| 393. C2 | C7×#3390 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#557 | 2 |
| C7×#3390 | 2 |
| C2×C7×#501 | 2 |
| C2×C7×#499 | 2 |
| C2×C7×#479 | 2 |
| C2×C7×#477 | 2 |
| C2×C7×#446 | 2 |
| C2×C7×#441 | 2 |
| C2×C4×C7×Q16 | 2 |
| C2×#3390 | 7 |