Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
996 conjugacy classes of subgroups; only the 384 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 384 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 |
|---|---|---|
| 3. C2×C4×C7×Dic3 | C2 | semidirect |
| 4. C2×C3×C4×Dic7 | C2 | semidirect |
| 5. C2×Dic3×Dic7 | C2 | semidirect |
| 6. C4×D21⋊C4 | C2 | direct (N × H) |
| 11. C2×C4×D21 | C4 | semidirect |
| 15. C2×D21⋊C4 | C4 | direct (N × H) |
| 17. C4×C7×Dic3 | C22 | semidirect |
| 18. C3×C4×Dic7 | C22 | semidirect |
| 19. Dic3×Dic7 | C22 | semidirect |
| 24. C2×C4×Dic7 | D3 | semidirect |
| 31. C2×C3×C4×C7 | C2×C4 | semidirect |
| 33. C2×Dic21 | C2×C4 | semidirect |
| 35. C4×D21 | C2×C4 | semidirect |
| 36. C2×C7×Dic3 | C2×C4 | semidirect |
| 38. C2×C3×Dic7 | C2×C4 | semidirect |
| 40. D21⋊C4 | C2×C4 | direct (N × H) |
| 52. C4×Dic7 | C2×D3 | semidirect |
| 57. C2×C4×Dic3 | D7 | semidirect |
| 62. C2×D21 | C42 | semidirect |
| 65. C3×C4×C7 | C22×C4 | semidirect |
| 66. Dic21 | C22×C4 | semidirect |
| 67. C3×Dic7 | C22×C4 | semidirect |
| 68. C7×Dic3 | C22×C4 | semidirect |
| 76. C2×C4×C7 | C4×D3 | semidirect |
| 80. C2×Dic7 | C4×D3 | semidirect |
| 95. C4×Dic3 | C2×D7 | semidirect |
| 96. C2×C3×C7 | C2×C42 | semidirect |
| 99. D21 | C2×C42 | semidirect |
| 113. C4×C7 | C2×C4×D3 | semidirect |
| 115. Dic7 | C2×C4×D3 | semidirect |
| 122. C2×C3×C4 | C4×D7 | semidirect |
| 126. C2×Dic3 | C4×D7 | semidirect |
| 130. C3×C7 | C22×C42 | semidirect |
| 143. C2×C7 | C42×D3 | semidirect |
| 154. C3×C4 | C2×C4×D7 | semidirect |
| 156. Dic3 | C2×C4×D7 | semidirect |
| 169. C2×C4 | D21⋊C4 | direct (N × H) |
| 171. C7 | C2×C42×D3 | semidirect |
| 172. C2×C3 | C42×D7 | semidirect |
| 185. C4 | C2×D21⋊C4 | direct (N × H) |
| 186. C3 | C2×C42×D7 | semidirect |
| 188. C2 | C4×D21⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D21 | 2 |
| C22×D21⋊C4 | 2 |
| C2×C4×C7×Dic3 | 2 |
| C2×C3×C4×Dic7 | 2 |
| C2×Dic3×Dic7 | 2 |
| C4×D21⋊C4 | 2 |
| C2×C42×D7 | 3 |
| C2×C42×D3 | 7 |