Finite Group DatabasebetaFinite Group DatabasebetaOrder 2016.
792 conjugacy classes of subgroups; only the 294 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 294 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. C2×C32×C4×D7 | C2 | semidirect |
| 3. C32×C7×C22⋊C4 | C2 | semidirect |
| 4. C32×C22⋊Dic7 | C2 | semidirect |
| 5. C32×(C2×D7)⋊C4 | C2 | semidirect |
| 6. C3×D7×C22⋊C4 | C3 | direct (N × H) |
| 9. C22×C32×D7 | C4 | semidirect |
| 12. C2×C32×C4×C7 | C22 | semidirect |
| 13. C2×C32×Dic7 | C22 | semidirect |
| 16. C2×C3×C4×D7 | C2×C3 | semidirect |
| 17. C3×C7×C22⋊C4 | C2×C3 | semidirect |
| 18. C3×C22⋊Dic7 | C2×C3 | semidirect |
| 19. C3×(C2×D7)⋊C4 | C2×C3 | semidirect |
| 22. C22×C32×C7 | C2×C4 | semidirect |
| 27. C2×C32×D7 | C2×C4 | semidirect |
| 31. D7×C22⋊C4 | C32 | direct (N × H) |
| 34. C22×C3×D7 | C3×C4 | semidirect |
| 37. C2×C3×C4×C7 | C22×C3 | semidirect |
| 38. C2×C3×Dic7 | C22×C3 | semidirect |
| 44. C32×C22⋊C4 | D7 | direct (N × H) |
| 49. C32×D7 | C22⋊C4 | direct (N × H) |
| 51. C2×C4×D7 | C2×C32 | semidirect |
| 52. C7×C22⋊C4 | C2×C32 | semidirect |
| 53. C22⋊Dic7 | C2×C32 | semidirect |
| 54. (C2×D7)⋊C4 | C2×C32 | semidirect |
| 57. C22×C3×C7 | C2×C3×C4 | semidirect |
| 62. C2×C3×D7 | C2×C3×C4 | semidirect |
| 73. C2×C32×C4 | C2×D7 | semidirect |
| 74. C32×C7 | C2×C22⋊C4 | semidirect |
| 77. C22×D7 | C32×C4 | semidirect |
| 80. C2×C4×C7 | C22×C32 | semidirect |
| 81. C2×Dic7 | C22×C32 | semidirect |
| 87. C3×C22⋊C4 | C3×D7 | direct (N × H) |
| 92. C3×D7 | C3×C22⋊C4 | direct (N × H) |
| 99. C22×C32 | C4×D7 | semidirect |
| 105. C22×C7 | C2×C32×C4 | semidirect |
| 110. C2×D7 | C2×C32×C4 | semidirect |
| 121. C2×C3×C4 | C2×C3×D7 | semidirect |
| 122. C3×C7 | C2×C3×C22⋊C4 | semidirect |
| 132. C22⋊C4 | C32×D7 | direct (N × H) |
| 137. D7 | C32×C22⋊C4 | direct (N × H) |
| 144. C22×C3 | C3×C4×D7 | semidirect |
| 148. C32 | D7×C22⋊C4 | direct (N × H) |
| 156. C2×C4 | C2×C32×D7 | semidirect |
| 157. C7 | C2×C32×C22⋊C4 | semidirect |
| 169. C22 | C32×C4×D7 | semidirect |
| 173. C3 | C3×D7×C22⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C32×D7 | 2 |
| C2×C32×C4×D7 | 2 |
| C32×C7×C22⋊C4 | 2 |
| C32×C22⋊Dic7 | 2 |
| C32×(C2×D7)⋊C4 | 2 |
| C3×D7×C22⋊C4 | 3 |
| C2×C32×C22⋊C4 | 7 |