Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
404 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#4248 | C2 | semidirect |
| 5. #10620670 | C2 | semidirect |
| 6. C3×C7⋊#95 | C2 | semidirect |
| 7. #10620529 | C2 | semidirect |
| 28. C7⋊#95 | D3 | semidirect |
| 37. C22×D3×C7 | Q8 | semidirect |
| 180. C22×D3 | Dic14 | semidirect |
| 200. C3×C7 | #393 | semidirect |
| 269. C7 | #4673 | semidirect |
| 298. C3 | #89719 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4248 | 2 |
| C2×C7×(C2×D3)⋊C4 | 2 |
| C2×(C2×D3)⋊Dic7 | 2 |
| #10620670 | 2 |
| C3×C7⋊#95 | 2 |
| #10620529 | 2 |
| #89719 | 3 |
| #4673 | 7 |