Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
216 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 216 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 |
|---|---|---|
| 1. #10621030 | C2 | semidirect |
| 3. #10620657 | C2 | semidirect |
| 5. C3×Dic7⋊C8 | C2 | semidirect |
| 6. #10620523 | C2 | semidirect |
| 25. Dic7⋊C8 | D3 | semidirect |
| 34. C7×D12 | Q8 | semidirect |
| 125. D12 | Dic14 | semidirect |
| 130. C3×C7 | #474 | semidirect |
| 170. C7 | #4846 | semidirect |
| 186. C3 | #89531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621030 | 2 |
| D12×Dic7 | 2 |
| #10620657 | 2 |
| C7×#821 | 2 |
| C3×Dic7⋊C8 | 2 |
| #10620523 | 2 |
| #10620502 | 2 |
| #89531 | 3 |
| #4846 | 7 |