Finite Group DatabasebetaFinite Group DatabasebetaOrder 2016.
780 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 222 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 |
|---|---|---|
| 1. C23×C32×D7 | C2 | semidirect |
| 2. C2×C32×C22⋊D7 | C2 | semidirect |
| 3. C2×C32×D28 | C2 | semidirect |
| 4. C32×C7×C22⋊C4 | C2 | semidirect |
| 5. C32×(C2×D7)⋊C4 | C2 | semidirect |
| 6. C3×#6445 | C3 | direct (N × H) |
| 11. C22×C32×D7 | C22 | semidirect |
| 12. C2×C32×C4×C7 | C22 | semidirect |
| 14. C2×C32×Dic7 | C22 | semidirect |
| 16. C23×C3×D7 | C2×C3 | semidirect |
| 17. C2×C3×C22⋊D7 | C2×C3 | semidirect |
| 18. C2×C3×D28 | C2×C3 | semidirect |
| 19. C3×C7×C22⋊C4 | C2×C3 | semidirect |
| 20. C3×(C2×D7)⋊C4 | C2×C3 | semidirect |
| 23. C22×C32×C7 | D4 | semidirect |
| 30. C2×C32×D7 | D4 | semidirect |
| 33. #6445 | C32 | direct (N × H) |
| 38. C22×C3×D7 | C22×C3 | semidirect |
| 39. C2×C3×C4×C7 | C22×C3 | semidirect |
| 41. C2×C3×Dic7 | C22×C3 | semidirect |
| 47. C32×C22⋊C4 | D7 | semidirect |
| 53. C23×D7 | C2×C32 | semidirect |
| 54. C2×C22⋊D7 | C2×C32 | semidirect |
| 55. C2×D28 | C2×C32 | semidirect |
| 56. C7×C22⋊C4 | C2×C32 | semidirect |
| 57. (C2×D7)⋊C4 | C2×C32 | semidirect |
| 60. C22×C3×C7 | C3×D4 | semidirect |
| 67. C2×C3×D7 | C3×D4 | semidirect |
| 78. C2×C32×C4 | C2×D7 | semidirect |
| 79. C32×C7 | #120 | semidirect |
| 84. C22×D7 | C22×C32 | semidirect |
| 85. C2×C4×C7 | C22×C32 | semidirect |
| 87. C2×Dic7 | C22×C32 | semidirect |
| 93. C3×C22⋊C4 | C3×D7 | semidirect |
| 106. C22×C32 | D28 | semidirect |
| 112. C22×C7 | C32×D4 | semidirect |
| 119. C2×D7 | C32×D4 | semidirect |
| 130. C2×C3×C4 | C2×C3×D7 | semidirect |
| 131. C3×C7 | C3×#120 | semidirect |
| 141. C22⋊C4 | C32×D7 | semidirect |
| 154. C22×C3 | C3×D28 | semidirect |
| 158. C32 | #6445 | direct (N × H) |
| 167. C2×C4 | C2×C32×D7 | semidirect |
| 168. C7 | C32×#120 | semidirect |
| 181. C22 | C32×D28 | semidirect |
| 185. C3 | C3×#6445 | 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×C22⋊D7 | 2 |
| C2×C32×D28 | 2 |
| C32×C7×C22⋊C4 | 2 |
| C32×(C2×D7)⋊C4 | 2 |
| C3×#6445 | 3 |
| C32×#120 | 7 |