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×Dic3×D7 | C2 | semidirect |
| 3. C2×C4⋊Dic21 | C2 | semidirect |
| 4. C2×C4×C7×Dic3 | C2 | semidirect |
| 5. C2×(C2×D7)⋊Dic3 | C2 | semidirect |
| 6. Dic3×D28 | C2 | direct (N × H) |
| 13. C2×C3×D28 | C4 | semidirect |
| 16. C2×Dic3×D7 | C22 | semidirect |
| 17. C4⋊Dic21 | C22 | semidirect |
| 18. C4×C7×Dic3 | C22 | semidirect |
| 19. (C2×D7)⋊Dic3 | C22 | semidirect |
| 30. C22×C3×D7 | C2×C4 | semidirect |
| 32. C2×C3×C4×C7 | C2×C4 | semidirect |
| 37. C2×C7×Dic3 | D4 | semidirect |
| 40. C3×D28 | C2×C4 | semidirect |
| 47. C2×D28 | Dic3 | direct (N × H) |
| 59. C2×C4×Dic3 | D7 | semidirect |
| 67. C2×C3×D7 | C22×C4 | semidirect |
| 68. C3×C4×C7 | C22×C4 | semidirect |
| 71. C7×Dic3 | C2×D4 | semidirect |
| 76. C22×D7 | C2×Dic3 | semidirect |
| 82. C2×C4×C7 | C2×Dic3 | semidirect |
| 86. D28 | C2×Dic3 | direct (N × H) |
| 99. C4×Dic3 | C2×D7 | semidirect |
| 100. C2×C3×C7 | C4×D4 | semidirect |
| 118. C2×D7 | C22×Dic3 | semidirect |
| 121. C4×C7 | C22×Dic3 | semidirect |
| 129. C2×C3×C4 | C4×D7 | semidirect |
| 135. C2×Dic3 | D28 | direct (N × H) |
| 138. C3×C7 | C2×C4×D4 | semidirect |
| 151. C2×C7 | D4×Dic3 | semidirect |
| 164. C3×C4 | C2×C4×D7 | semidirect |
| 167. Dic3 | C2×D28 | direct (N × H) |
| 181. C2×C4 | Dic3×D7 | semidirect |
| 183. C7 | C2×D4×Dic3 | semidirect |
| 185. C2×C3 | C4×D28 | semidirect |
| 200. C4 | C2×Dic3×D7 | semidirect |
| 201. C3 | C2×C4×D28 | semidirect |
| 203. C2 | Dic3×D28 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D28 | 2 |
| C22×Dic3×D7 | 2 |
| C2×C4⋊Dic21 | 2 |
| C2×C4×C7×Dic3 | 2 |
| C2×(C2×D7)⋊Dic3 | 2 |
| Dic3×D28 | 2 |
| C2×C4×D28 | 3 |
| C2×D4×Dic3 | 7 |