Finite Group DatabasebetaFinite Group DatabasebetaOrder 1008.
232 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 232 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×C3×D21 | C2 | semidirect |
| 2. C2×C3×D3×D7 | C2 | semidirect |
| 3. C3×C7×#67 | C2 | semidirect |
| 4. C32×C22⋊D7 | C2 | semidirect |
| 5. C3×#4247 | C2 | semidirect |
| 6. C3×#4246 | C2 | semidirect |
| 7. C3×D21⋊C4 | C2 | semidirect |
| 9. #66694 | C3 | direct (N × H) |
| 10. C22×C32×C7 | C22 | semidirect |
| 13. C2×C3×D21 | C22 | semidirect |
| 14. C2×C3×D3×C7 | C22 | semidirect |
| 15. C2×C32×D7 | C22 | semidirect |
| 17. C3×C7×Dic3 | C22 | semidirect |
| 18. C32×Dic7 | C22 | semidirect |
| 19. C22×D21 | C2×C3 | semidirect |
| 22. C2×D3×D7 | C2×C3 | semidirect |
| 24. C7×#67 | C2×C3 | semidirect |
| 27. C3×C22⋊D7 | D3 | semidirect |
| 28. C3×C22⋊D7 | C2×C3 | semidirect |
| 31. #4247 | C2×C3 | semidirect |
| 32. #4246 | C2×C3 | semidirect |
| 33. D21⋊C4 | C2×C3 | semidirect |
| 38. C3×D21 | D4 | semidirect |
| 44. C22×C3×C7 | C2×D3 | semidirect |
| 45. C22×C3×C7 | C22×C3 | semidirect |
| 48. C2×D21 | C22×C3 | semidirect |
| 49. C2×D3×C7 | C22×C3 | semidirect |
| 55. C2×C3×D7 | C2×D3 | semidirect |
| 56. C2×C3×D7 | C22×C3 | semidirect |
| 60. C3×Dic7 | C2×D3 | semidirect |
| 61. C3×Dic7 | C22×C3 | semidirect |
| 62. C7×Dic3 | C22×C3 | semidirect |
| 67. C3×#67 | D7 | semidirect |
| 70. C32×C7 | C2×D4 | semidirect |
| 75. C22⋊D7 | C3×D3 | semidirect |
| 88. D21 | C3×D4 | semidirect |
| 96. C22×C32 | C2×D7 | semidirect |
| 101. C2×C3×D3 | C2×D7 | semidirect |
| 103. C3×Dic3 | C2×D7 | semidirect |
| 105. C22×C7 | C2×C3×D3 | semidirect |
| 110. C2×D7 | C2×C3×D3 | semidirect |
| 112. Dic7 | C2×C3×D3 | semidirect |
| 125. #67 | C3×D7 | semidirect |
| 129. C3×C7 | D3×D4 | semidirect |
| 130. C3×C7 | C2×C3×D4 | semidirect |
| 153. C22×C3 | D3×D7 | semidirect |
| 154. C22×C3 | C2×C3×D7 | semidirect |
| 159. C2×D3 | C2×C3×D7 | semidirect |
| 164. Dic3 | C2×C3×D7 | semidirect |
| 165. C32 | D4×D7 | semidirect |
| 173. C7 | C3×D3×D4 | semidirect |
| 195. C22 | C3×D3×D7 | semidirect |
| 199. C3 | #66694 | direct (N × H) |
| 200. C3 | C3×D4×D7 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D21 | 2 |
| C2×C3×D3×D7 | 2 |
| C3×C7×#67 | 2 |
| C32×C22⋊D7 | 2 |
| C3×#4247 | 2 |
| C3×#4246 | 2 |
| C3×D21⋊C4 | 2 |
| C3×D4×D7 | 3 |
| #66694 | 3 |
| C3×D3×D4 | 7 |