Finite Group DatabasebetaFinite Group DatabasebetaOrder 1680.
216 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 68 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. C22×C5×D21 | C2 | semidirect |
| 2. C2×C5×D3×D7 | C2 | semidirect |
| 3. C5×C7×#67 | C2 | semidirect |
| 4. C3×C5×C22⋊D7 | C2 | semidirect |
| 5. C5×#4247 | C2 | semidirect |
| 6. C5×#4246 | C2 | semidirect |
| 7. C5×D21⋊C4 | C2 | semidirect |
| 9. C22×C3×C5×C7 | C22 | semidirect |
| 12. C2×C5×D21 | C22 | semidirect |
| 13. C2×C5×D3×C7 | C22 | semidirect |
| 14. C2×C3×C5×D7 | C22 | semidirect |
| 16. C5×C7×Dic3 | C22 | semidirect |
| 17. C3×C5×Dic7 | C22 | semidirect |
| 18. #66694 | C5 | direct (N × H) |
| 23. C5×C22⋊D7 | D3 | semidirect |
| 30. C5×D21 | D4 | semidirect |
| 33. C22×D21 | C2×C5 | semidirect |
| 34. C2×D3×D7 | C2×C5 | semidirect |
| 35. C7×#67 | C2×C5 | semidirect |
| 36. C3×C22⋊D7 | C2×C5 | semidirect |
| 37. #4247 | C2×C5 | semidirect |
| 38. #4246 | C2×C5 | semidirect |
| 39. D21⋊C4 | C2×C5 | semidirect |
| 41. C22×C5×C7 | C2×D3 | semidirect |
| 46. C2×C5×D7 | C2×D3 | semidirect |
| 48. C5×Dic7 | C2×D3 | semidirect |
| 53. C5×#67 | D7 | semidirect |
| 57. C3×C5×C7 | C2×D4 | semidirect |
| 58. C22×C3×C7 | C22×C5 | semidirect |
| 61. C2×D21 | C22×C5 | semidirect |
| 62. C2×D3×C7 | C22×C5 | semidirect |
| 63. C2×C3×D7 | C22×C5 | semidirect |
| 65. C3×Dic7 | C22×C5 | semidirect |
| 66. C7×Dic3 | C22×C5 | semidirect |
| 75. C22×C3×C5 | C2×D7 | semidirect |
| 80. C2×C5×D3 | C2×D7 | semidirect |
| 82. C5×Dic3 | C2×D7 | semidirect |
| 87. C22⋊D7 | C5×D3 | semidirect |
| 94. D21 | C5×D4 | semidirect |
| 104. C5×C7 | D3×D4 | semidirect |
| 112. C22×C7 | C2×C5×D3 | semidirect |
| 117. C2×D7 | C2×C5×D3 | semidirect |
| 119. Dic7 | C2×C5×D3 | semidirect |
| 124. #67 | C5×D7 | semidirect |
| 127. C3×C7 | C2×C5×D4 | semidirect |
| 134. C22×C5 | D3×D7 | semidirect |
| 138. C3×C5 | D4×D7 | semidirect |
| 146. C22×C3 | C2×C5×D7 | semidirect |
| 151. C2×D3 | C2×C5×D7 | semidirect |
| 153. Dic3 | C2×C5×D7 | semidirect |
| 167. C7 | C5×D3×D4 | semidirect |
| 174. C5 | #66694 | direct (N × H) |
| 181. C22 | C5×D3×D7 | semidirect |
| 184. C3 | C5×D4×D7 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D21 | 2 |
| C2×C5×D3×D7 | 2 |
| C5×C7×#67 | 2 |
| C3×C5×C22⋊D7 | 2 |
| C5×#4247 | 2 |
| C5×#4246 | 2 |
| C5×D21⋊C4 | 2 |
| C5×D4×D7 | 3 |
| #66694 | 5 |
| C5×D3×D4 | 7 |