Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
540 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 160 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 |
|---|---|---|
| 2. C22×C3×Dic14 | C2 | semidirect |
| 3. C7×#926 | C2 | semidirect |
| 4. #10621108 | C2 | semidirect |
| 5. #10620952 | C2 | semidirect |
| 6. #10620951 | C2 | semidirect |
| 7. #10620936 | C2 | semidirect |
| 25. C22×Dic14 | D3 | semidirect |
| 68. #926 | D7 | semidirect |
| 146. C3×C7 | #536 | semidirect |
| 191. C7 | #5816 | semidirect |
| 206. C3 | #90217 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66728 | 2 |
| C22×C3×Dic14 | 2 |
| C7×#926 | 2 |
| #10621108 | 2 |
| #10620952 | 2 |
| #10620951 | 2 |
| #10620936 | 2 |
| #90217 | 3 |
| #5816 | 7 |