Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
216 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 76 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. C3×#6432 | C2 | semidirect |
| 3. C4⋊(C3⋊(C7⋊C8)) | C2 | semidirect |
| 4. #10620524 | C2 | semidirect |
| 17. #6432 | D3 | semidirect |
| 28. C7×D12 | Q8 | semidirect |
| 105. D12 | Dic14 | semidirect |
| 108. C3×C7 | #474 | semidirect |
| 143. C7 | #5087 | semidirect |
| 158. C3 | #89779 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C7×D12 | 2 |
| C3×#6432 | 2 |
| C4⋊(C3⋊(C7⋊C8)) | 2 |
| #10620524 | 2 |
| #10620501 | 2 |
| #89779 | 3 |
| #5087 | 7 |