Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
476 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 108 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. C2×C3×Dic7⋊C4 | C2 | semidirect |
| 3. C2×(C2×D3)⋊Dic7 | C2 | semidirect |
| 4. C2×(C2×D3)⋊Dic7 | C2 | semidirect |
| 5. #10620670 | C2 | semidirect |
| 20. C2×Dic7⋊C4 | D3 | semidirect |
| 41. C2×C3×Dic7 | D4 | semidirect |
| 92. C2×Dic7 | D12 | semidirect |
| 149. C3×C7 | #394 | semidirect |
| 201. C7 | #4991 | semidirect |
| 224. C3 | #89994 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×D12 | 2 |
| C2×C3×Dic7⋊C4 | 2 |
| C2×(C2×D3)⋊Dic7 | 2 |
| #10620670 | 2 |
| #89994 | 3 |
| #4991 | 7 |