Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
1348 conjugacy classes of subgroups; only the 283 normal subgroups are shown.
This group has 1348 conjugacy classes of subgroups — too many to draw. Only its 283 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×C4×D21 | C2 | semidirect |
| 3. C2×C3×C7×C22⋊C4 | C2 | semidirect |
| 4. C2×#66636 | C2 | semidirect |
| 5. C2×#66631 | C2 | semidirect |
| 6. C22⋊C4×D21 | C2 | direct (N × H) |
| 10. C23×D21 | C4 | semidirect |
| 14. C22×C3×C4×C7 | C22 | semidirect |
| 15. C22×Dic21 | C22 | semidirect |
| 17. C2×C4×D21 | C22 | semidirect |
| 18. C3×C7×C22⋊C4 | C22 | semidirect |
| 19. #66636 | C22 | semidirect |
| 20. #66631 | C22 | semidirect |
| 23. C2×C7×C22⋊C4 | D3 | semidirect |
| 29. C23×C3×C7 | C2×C4 | semidirect |
| 36. C22×D21 | C2×C4 | semidirect |
| 37. C22×D21 | C2×C4 | semidirect |
| 42. C2×C3×C4×C7 | C23 | semidirect |
| 44. C2×Dic21 | C23 | semidirect |
| 52. C22×C4×C7 | C2×D3 | semidirect |
| 56. C7×C22⋊C4 | C2×D3 | semidirect |
| 61. C2×C3×C22⋊C4 | D7 | semidirect |
| 68. C22×C3×C7 | C22×C4 | semidirect |
| 74. C2×D21 | C22⋊C4 | direct (N × H) |
| 76. C2×D21 | C22×C4 | semidirect |
| 82. C23×C7 | C4×D3 | semidirect |
| 95. C2×C4×C7 | C22×D3 | semidirect |
| 105. C22×C3×C4 | C2×D7 | semidirect |
| 109. C3×C22⋊C4 | C2×D7 | semidirect |
| 113. C2×C3×C7 | C2×C22⋊C4 | semidirect |
| 117. D21 | C2×C22⋊C4 | direct (N × H) |
| 123. C2×C22⋊C4 | D21 | direct (N × H) |
| 127. C22×C7 | C2×C4×D3 | semidirect |
| 140. C23×C3 | C4×D7 | semidirect |
| 153. C2×C3×C4 | C22×D7 | semidirect |
| 157. C3×C7 | C22×C22⋊C4 | semidirect |
| 167. C22×C4 | C2×D21 | semidirect |
| 170. C22⋊C4 | C2×D21 | direct (N × H) |
| 172. C2×C7 | D3×C22⋊C4 | semidirect |
| 180. C22×C3 | C2×C4×D7 | semidirect |
| 202. C23 | C4×D21 | semidirect |
| 209. C2×C4 | C22×D21 | semidirect |
| 210. C7 | C2×D3×C22⋊C4 | semidirect |
| 212. C2×C3 | D7×C22⋊C4 | semidirect |
| 227. C22 | C2×C4×D21 | semidirect |
| 232. C3 | C2×D7×C22⋊C4 | semidirect |
| 236. C2 | C22⋊C4×D21 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×D21 | 2 |
| C22×C4×D21 | 2 |
| C2×C3×C7×C22⋊C4 | 2 |
| C2×#66636 | 2 |
| C2×#66631 | 2 |
| C22⋊C4×D21 | 2 |
| C2×D7×C22⋊C4 | 3 |
| C2×D3×C22⋊C4 | 7 |