Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
476 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 126 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×C7×C4⋊C4 | C2 | semidirect |
| 3. C2×C7×(C2×D3)⋊C4 | C2 | semidirect |
| 4. C2×C7×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C7×C3⋊#95 | C2 | semidirect |
| 18. C2×C7×C4⋊C4 | D3 | semidirect |
| 22. #4991 | C7 | direct (N × H) |
| 37. C2×C3×C4×C7 | D4 | semidirect |
| 53. C2×C3×C4⋊C4 | C2×C7 | semidirect |
| 54. C2×(C2×D3)⋊C4 | C2×C7 | semidirect |
| 55. C2×(C2×D3)⋊C4 | C2×C7 | semidirect |
| 56. C3⋊#95 | C2×C7 | semidirect |
| 91. C2×C4×C7 | D12 | semidirect |
| 110. C2×C4⋊C4 | D3×C7 | semidirect |
| 144. C2×C3×C4 | C7×D4 | semidirect |
| 149. C3×C7 | #394 | semidirect |
| 199. C2×C4 | C7×D12 | semidirect |
| 201. C7 | #4991 | 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×C3×C7×C4⋊C4 | 2 |
| C2×C7×(C2×D3)⋊C4 | 2 |
| C7×C3⋊#95 | 2 |
| C7×#394 | 3 |
| #4991 | 7 |