Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
476 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 122 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×C7×(C2×D3)⋊C4 | C2 | semidirect |
| 3. C2×C7×(C2×D3)⋊C4 | C2 | semidirect |
| 4. C2×C7×Dic3⋊C4 | C2 | semidirect |
| 5. C3×C7×#95 | C2 | semidirect |
| 21. C7×#95 | D3 | semidirect |
| 22. #4672 | C7 | direct (N × H) |
| 40. C2×C7×Dic3 | D4 | semidirect |
| 53. C2×(C2×D3)⋊C4 | C2×C7 | semidirect |
| 54. C2×(C2×D3)⋊C4 | C2×C7 | semidirect |
| 55. C2×Dic3⋊C4 | C2×C7 | semidirect |
| 56. C3×#95 | C2×C7 | semidirect |
| 113. #95 | D3×C7 | semidirect |
| 147. C2×Dic3 | C7×D4 | semidirect |
| 149. C3×C7 | #394 | semidirect |
| 201. C7 | #4672 | direct (N × H) |
| 224. C3 | C7×#394 | 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×C7×(C2×D3)⋊C4 | 2 |
| C2×C7×Dic3⋊C4 | 2 |
| C3×C7×#95 | 2 |
| C7×#394 | 3 |
| #4672 | 7 |