Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1766 conjugacy classes of subgroups.
The subgroup lattice has 336 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×#3383 | C2 | direct (N × H) |
| 38. C2×#3383 | C7 | direct (N × H) |
| 42. C2×C7×Q16 | Q8 | semidirect |
| 84. #3383 | C2×C7 | direct (N × H) |
| 108. C7×Q16 | C2×Q8 | semidirect |
| 190. C2×Q16 | C7×Q8 | semidirect |
| 261. Q16 | C2×C7×Q8 | semidirect |
| 285. C2×C7 | #3383 | direct (N × H) |
| 316. C7 | C2×#3383 | direct (N × H) |
| 331. C2 | C7×#3383 | 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×#3383 | 2 |
| C2×C7×#500 | 2 |
| C2×C7×#499 | 2 |
| C2×C7×#479 | 2 |
| C2×C7×#475 | 2 |
| C2×C7×C8×Q8 | 2 |
| C2×C4×C7×Q16 | 2 |
| C2×#3383 | 7 |