Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
260 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 66 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. C7×#936 | C2 | semidirect |
| 3. C2×C3×#1142 | C2 | semidirect |
| 4. #10620936 | C2 | semidirect |
| 5. C2×#66569 | C2 | semidirect |
| 6. C2×#66568 | C2 | semidirect |
| 7. Dic3×C7⋊C8 | C2 | semidirect |
| 25. C2×#1142 | D3 | semidirect |
| 62. #936 | D7 | semidirect |
| 143. C3×C7 | #495 | semidirect |
| 187. C7 | #5168 | semidirect |
| 202. C3 | #89831 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66632 | 2 |
| C7×#936 | 2 |
| C2×C3×#1142 | 2 |
| #10620936 | 2 |
| C2×#66569 | 2 |
| C2×#66568 | 2 |
| Dic3×C7⋊C8 | 2 |
| #89831 | 3 |
| #5168 | 7 |