Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
2198 conjugacy classes of subgroups.
The subgroup lattice has 374 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #11739655 | C2 | semidirect |
| 4. #11739654 | C2 | semidirect |
| 5. #11739649 | C2 | semidirect |
| 6. #11739647 | C2 | semidirect |
| 7. #11739494 | C2 | semidirect |
| 24. #89772 | C22 | semidirect |
| 25. #89771 | C22 | semidirect |
| 26. #89769 | C22 | semidirect |
| 27. #89698 | C22 | semidirect |
| 28. #89697 | C22 | semidirect |
| 29. #89696 | C22 | semidirect |
| 30. C4×#1136 | C22 | semidirect |
| 71. C4⋊(C7⋊C8) | C23 | semidirect |
| 72. #6377 | C23 | semidirect |
| 73. C4×C7⋊C8 | C23 | semidirect |
| 345. C7 | #60124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×#117 | 2 |
| C2×#89979 | 2 |
| #11739655 | 2 |
| #11739654 | 2 |
| #11739649 | 2 |
| #11739647 | 2 |
| #11739494 | 2 |
| #60124 | 7 |