Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
10930 conjugacy classes of subgroups.
The subgroup lattice has 140 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator | C2 | C25×C4×C7 |
| Frattini, cosocle | C22 | C26×C7 |
| prime radical | C22×C7×2−1+4 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×C7×2−1+4 | C2 | semidirect |
| 3. C7×#3428 | C2 | semidirect |
| 4. C2×C7×#519 | C2 | semidirect |
| 5. C2×C7×2−1+4 | C4 | semidirect |
| 9. C7×#520 | C22 | semidirect |
| 11. C7×#519 | C22 | semidirect |
| 13. C4×C7×#41 | C22 | semidirect |
| 14. C2×C4×C7×Q8 | C22 | semidirect |
| 16. #62653 | C7 | direct (N × H) |
| 17. C7×2−1+4 | C2×C4 | semidirect |
| 18. C2×C7×#41 | C2×C4 | semidirect |
| 20. C22×C7×Q8 | C2×C4 | semidirect |
| 33. C4×2−1+4 | C2×C7 | semidirect |
| 34. #3428 | C2×C7 | semidirect |
| 35. C2×#519 | C2×C7 | semidirect |
| 51. C2×2−1+4 | C4×C7 | semidirect |
| 55. #520 | C22×C7 | semidirect |
| 57. #519 | C22×C7 | semidirect |
| 59. C4×#41 | C22×C7 | semidirect |
| 60. C2×C4×Q8 | C22×C7 | semidirect |
| 73. 2−1+4 | C2×C4×C7 | semidirect |
| 74. C2×#41 | C2×C4×C7 | semidirect |
| 76. C22×Q8 | C2×C4×C7 | semidirect |
| 126. C7 | #62653 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×2−1+4 | 2 |
| C4×C7×2−1+4 | 2 |
| C7×#3428 | 2 |
| C2×C7×#519 | 2 |
| #62653 | 7 |