Finite Group DatabasebetaFinite Group DatabasebetaOrder 2352.
264 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 264 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×C7×D21 | C2 | semidirect |
| 2. C2×D3×C7×D7 | C2 | semidirect |
| 3. C72×#67 | C2 | semidirect |
| 4. C3×C7×C22⋊D7 | C2 | semidirect |
| 5. C7×#4247 | C2 | semidirect |
| 6. C7×#4246 | C2 | semidirect |
| 7. C7×D21⋊C4 | C2 | semidirect |
| 9. C22×C3×C72 | C22 | semidirect |
| 12. C2×C7×D21 | C22 | semidirect |
| 13. C2×D3×C72 | C22 | semidirect |
| 14. C2×C3×C7×D7 | C22 | semidirect |
| 16. C72×Dic3 | C22 | semidirect |
| 17. C3×C7×Dic7 | C22 | semidirect |
| 22. C7×C22⋊D7 | D3 | semidirect |
| 26. #66694 | C7 | direct (N × H) |
| 30. C7×D21 | D4 | semidirect |
| 34. C22×C72 | C2×D3 | semidirect |
| 39. C2×C7×D7 | C2×D3 | semidirect |
| 41. C7×Dic7 | C2×D3 | semidirect |
| 42. C22×D21 | C2×C7 | semidirect |
| 45. C2×D3×D7 | C2×C7 | semidirect |
| 49. C7×#67 | D7 | semidirect |
| 50. C7×#67 | C2×C7 | semidirect |
| 53. C3×C22⋊D7 | C2×C7 | semidirect |
| 54. #4247 | C2×C7 | semidirect |
| 55. #4246 | C2×C7 | semidirect |
| 56. D21⋊C4 | C2×C7 | semidirect |
| 57. C3×C72 | C2×D4 | semidirect |
| 68. C22×C3×C7 | C2×D7 | semidirect |
| 69. C22×C3×C7 | C22×C7 | semidirect |
| 72. C2×D21 | C22×C7 | semidirect |
| 78. C2×D3×C7 | C2×D7 | semidirect |
| 79. C2×D3×C7 | C22×C7 | semidirect |
| 80. C2×C3×D7 | C22×C7 | semidirect |
| 83. C3×Dic7 | C22×C7 | semidirect |
| 85. C7×Dic3 | C2×D7 | semidirect |
| 86. C7×Dic3 | C22×C7 | semidirect |
| 99. C22⋊D7 | D3×C7 | semidirect |
| 102. C72 | D3×D4 | semidirect |
| 112. D21 | C7×D4 | semidirect |
| 128. C22×C7 | D3×D7 | semidirect |
| 129. C22×C7 | C2×D3×C7 | semidirect |
| 134. C2×D7 | C2×D3×C7 | semidirect |
| 139. Dic7 | C2×D3×C7 | semidirect |
| 144. #67 | C7×D7 | semidirect |
| 148. C3×C7 | D4×D7 | semidirect |
| 149. C3×C7 | C2×C7×D4 | semidirect |
| 167. C22×C3 | C2×C7×D7 | semidirect |
| 172. C2×D3 | C2×C7×D7 | semidirect |
| 174. Dic3 | C2×C7×D7 | semidirect |
| 183. C7 | #66694 | direct (N × H) |
| 184. C7 | D3×C7×D4 | semidirect |
| 197. C22 | D3×C7×D7 | semidirect |
| 200. C3 | C7×D4×D7 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×D21 | 2 |
| C2×D3×C7×D7 | 2 |
| C72×#67 | 2 |
| C3×C7×C22⋊D7 | 2 |
| C7×#4247 | 2 |
| C7×#4246 | 2 |
| C7×D21⋊C4 | 2 |
| C7×D4×D7 | 3 |
| D3×C7×D4 | 7 |
| #66694 | 7 |