Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
852 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 288 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. C22×D3×Dic7 | C2 | semidirect |
| 3. C2×C4⋊Dic21 | C2 | semidirect |
| 4. C2×C3×C4×Dic7 | C2 | semidirect |
| 5. C2×(C2×D3)⋊Dic7 | C2 | semidirect |
| 6. D12×Dic7 | C2 | direct (N × H) |
| 11. C2×C7×D12 | C4 | semidirect |
| 16. C2×D3×Dic7 | C22 | semidirect |
| 17. C4⋊Dic21 | C22 | semidirect |
| 18. C3×C4×Dic7 | C22 | semidirect |
| 19. (C2×D3)⋊Dic7 | C22 | semidirect |
| 25. C2×C4×Dic7 | D3 | semidirect |
| 30. C22×D3×C7 | C2×C4 | semidirect |
| 32. C2×C3×C4×C7 | C2×C4 | semidirect |
| 36. C7×D12 | C2×C4 | semidirect |
| 38. C2×C3×Dic7 | D4 | semidirect |
| 53. C4×Dic7 | C2×D3 | semidirect |
| 67. C2×D3×C7 | C22×C4 | semidirect |
| 68. C3×C4×C7 | C22×C4 | semidirect |
| 71. C3×Dic7 | C2×D4 | semidirect |
| 79. C2×C4×C7 | C4×D3 | semidirect |
| 85. C2×Dic7 | D12 | direct (N × H) |
| 93. C2×D12 | Dic7 | direct (N × H) |
| 100. C2×C3×C7 | C4×D4 | semidirect |
| 119. C4×C7 | C2×C4×D3 | semidirect |
| 122. Dic7 | C2×D12 | direct (N × H) |
| 126. C22×D3 | C2×Dic7 | semidirect |
| 132. C2×C3×C4 | C2×Dic7 | semidirect |
| 136. D12 | C2×Dic7 | direct (N × H) |
| 138. C3×C7 | C2×C4×D4 | semidirect |
| 152. C2×C7 | C4×D12 | semidirect |
| 163. C2×D3 | C22×Dic7 | semidirect |
| 166. C3×C4 | C22×Dic7 | semidirect |
| 181. C2×C4 | D3×Dic7 | semidirect |
| 183. C7 | C2×C4×D12 | semidirect |
| 184. C2×C3 | D4×Dic7 | semidirect |
| 200. C4 | C2×D3×Dic7 | semidirect |
| 201. C3 | C2×D4×Dic7 | semidirect |
| 203. C2 | D12×Dic7 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×D12 | 2 |
| C22×D3×Dic7 | 2 |
| C2×C4⋊Dic21 | 2 |
| C2×C3×C4×Dic7 | 2 |
| C2×(C2×D3)⋊Dic7 | 2 |
| D12×Dic7 | 2 |
| C2×D4×Dic7 | 3 |
| C2×C4×D12 | 7 |