Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
918 conjugacy classes of subgroups.
The subgroup lattice has 334 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | #121 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C24×C7 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C23×C4×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C7×#1951 | C2 | direct (N × H) |
| 12. C2×C7×#108 | C4 | semidirect |
| 27. C2×#1951 | C7 | direct (N × H) |
| 59. C7×#108 | C2×C4 | semidirect |
| 70. #1951 | C2×C7 | direct (N × H) |
| 120. C2×#108 | C4×C7 | semidirect |
| 200. #108 | C2×C4×C7 | semidirect |
| 271. C2×C7 | #1951 | direct (N × H) |
| 308. C7 | C2×#1951 | direct (N × H) |
| 330. C2 | C7×#1951 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×#108 | 2 |
| C2×C7×#428 | 2 |
| C22×C7×#106 | 2 |
| C2×C7×#405 | 2 |
| C7×#1951 | 2 |
| C2×C7×#343 | 2 |
| C2×#1951 | 7 |