Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
1348 conjugacy classes of subgroups; only the 494 normal subgroups are shown.
This group has 1348 conjugacy classes of subgroups — too many to draw. Only its 494 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. C23×C3×C4×C7 | C2 | semidirect |
| 3. C23×C7×Dic3 | C2 | semidirect |
| 4. C2×C7×(C2×D3)⋊C4 | C2 | direct (N × H) |
| 9. C23×D3×C7 | C4 | semidirect |
| 12. C22×C3×C4×C7 | C22 | semidirect |
| 14. C22×C7×Dic3 | C22 | semidirect |
| 15. C7×(C2×D3)⋊C4 | C22 | direct (N × H) |
| 18. C23×C4×C7 | D3 | semidirect |
| 20. C22×(C2×D3)⋊C4 | C7 | direct (N × H) |
| 28. C22×D3×C7 | C2×C4 | semidirect |
| 31. C2×C3×C4×C7 | C23 | semidirect |
| 33. C2×C7×Dic3 | C23 | semidirect |
| 42. C22×C4×C7 | C2×D3 | semidirect |
| 45. C23×C3×C4 | C2×C7 | semidirect |
| 46. C23×Dic3 | C2×C7 | semidirect |
| 47. C2×(C2×D3)⋊C4 | C2×C7 | direct (N × H) |
| 48. C22×C3×C7 | C22⋊C4 | semidirect |
| 56. C2×D3×C7 | C22×C4 | semidirect |
| 72. C2×C4×C7 | C22×D3 | semidirect |
| 76. C23×D3 | C4×C7 | semidirect |
| 79. C22×C3×C4 | C22×C7 | semidirect |
| 81. C22×Dic3 | C22×C7 | semidirect |
| 82. (C2×D3)⋊C4 | C22×C7 | direct (N × H) |
| 83. C2×C3×C7 | C2×C22⋊C4 | semidirect |
| 90. C23×C4 | D3×C7 | semidirect |
| 96. C22×C7 | (C2×D3)⋊C4 | direct (N × H) |
| 110. C22×D3 | C2×C4×C7 | semidirect |
| 113. C2×C3×C4 | C23×C7 | semidirect |
| 115. C2×Dic3 | C23×C7 | semidirect |
| 116. C3×C7 | C22×C22⋊C4 | semidirect |
| 125. C22×C4 | C2×D3×C7 | semidirect |
| 128. C2×C7 | C2×(C2×D3)⋊C4 | direct (N × H) |
| 132. C22×C3 | C7×C22⋊C4 | semidirect |
| 140. C2×D3 | C22×C4×C7 | semidirect |
| 155. C2×C4 | C22×D3×C7 | semidirect |
| 156. C7 | C22×(C2×D3)⋊C4 | direct (N × H) |
| 157. C2×C3 | C2×C7×C22⋊C4 | semidirect |
| 166. C22 | C7×(C2×D3)⋊C4 | direct (N × H) |
| 173. C3 | C22×C7×C22⋊C4 | semidirect |
| 175. C2 | C2×C7×(C2×D3)⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×D3×C7 | 2 |
| C23×C3×C4×C7 | 2 |
| C23×C7×Dic3 | 2 |
| C2×C7×(C2×D3)⋊C4 | 2 |
| C22×C7×C22⋊C4 | 3 |
| C22×(C2×D3)⋊C4 | 7 |