Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
236 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 68 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. #10621031 | C2 | semidirect |
| 3. #10620671 | C2 | semidirect |
| 4. C3×#6406 | C2 | semidirect |
| 5. #10620502 | C2 | semidirect |
| 6. #10620501 | C2 | semidirect |
| 7. Dic3×C7⋊C8 | C2 | semidirect |
| 25. #6406 | D3 | semidirect |
| 144. C3×C7 | #486 | semidirect |
| 190. C7 | #4760 | semidirect |
| 209. C3 | #89842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#940 | 2 |
| #10621031 | 2 |
| #10620671 | 2 |
| C3×#6406 | 2 |
| #10620502 | 2 |
| #10620501 | 2 |
| Dic3×C7⋊C8 | 2 |
| #89842 | 3 |
| #4760 | 7 |