Finite Group DatabasebetaFinite Group DatabasebetaOrder 4704.
2360 conjugacy classes of subgroups; only the 498 normal subgroups are shown.
This group has 2360 conjugacy classes of subgroups — too many to draw. Only its 498 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. C2×C3×C22⋊(C7⋊D7) | C2 | semidirect |
| 2. C23×C3×C7⋊D7 | C2 | semidirect |
| 3. C2×C3×C4⋊(C7⋊D7) | C2 | semidirect |
| 4. C2×C3×C72×D4 | C2 | semidirect |
| 5. C3×D4×C7⋊D7 | C2 | direct (N × H) |
| 6. C2×C3×C4×C7⋊D7 | C2 | semidirect |
| 7. C2×D4×C7⋊D7 | C3 | direct (N × H) |
| 8. C23×C3×C72 | C22 | semidirect |
| 11. C22×C3×C7⋊D7 | C22 | semidirect |
| 12. C22×C3×C7⋊D7 | C22 | semidirect |
| 13. C3×C72×D4 | C22 | semidirect |
| 14. C2×C3×C4×C72 | C22 | semidirect |
| 15. C3×C22⋊(C7⋊D7) | C22 | semidirect |
| 16. C2×C3×C7⋊Dic7 | C22 | semidirect |
| 17. C3×C4⋊(C7⋊D7) | C22 | semidirect |
| 18. C3×C4×C7⋊D7 | C22 | semidirect |
| 19. C23×C7⋊D7 | C2×C3 | semidirect |
| 20. C2×C72×D4 | C2×C3 | semidirect |
| 21. C2×C22⋊(C7⋊D7) | C2×C3 | semidirect |
| 22. D4×C7⋊D7 | C2×C3 | direct (N × H) |
| 23. C2×C4⋊(C7⋊D7) | C2×C3 | semidirect |
| 24. C2×C4×C7⋊D7 | C2×C3 | semidirect |
| 28. C22×C3×C72 | C23 | semidirect |
| 31. C2×C3×C7⋊D7 | D4 | direct (N × H) |
| 33. C2×C3×C7⋊D7 | C23 | semidirect |
| 34. C3×C4×C72 | C23 | semidirect |
| 35. C3×C7⋊Dic7 | C23 | semidirect |
| 36. C23×C72 | C22×C3 | semidirect |
| 39. C22×C7⋊D7 | C22×C3 | semidirect |
| 40. C22×C7⋊D7 | C22×C3 | semidirect |
| 41. C72×D4 | C22×C3 | semidirect |
| 42. C2×C4×C72 | C22×C3 | semidirect |
| 43. C22⋊(C7⋊D7) | C22×C3 | semidirect |
| 44. C2×C7⋊Dic7 | C22×C3 | semidirect |
| 45. C4⋊(C7⋊D7) | C22×C3 | semidirect |
| 46. C4×C7⋊D7 | C22×C3 | semidirect |
| 48. C2×C3×C7×D4 | D7 | semidirect |
| 54. C2×C3×C72 | C2×D4 | semidirect |
| 57. C3×C7⋊D7 | C2×D4 | direct (N × H) |
| 61. C22×C72 | C23×C3 | semidirect |
| 64. C2×C7⋊D7 | C3×D4 | direct (N × H) |
| 66. C2×C7⋊D7 | C23×C3 | semidirect |
| 67. C4×C72 | C23×C3 | semidirect |
| 68. C7⋊Dic7 | C23×C3 | semidirect |
| 69. C23×C3×C7 | C2×D7 | semidirect |
| 74. C3×C7×D4 | C2×D7 | semidirect |
| 75. C2×C3×C4×C7 | C2×D7 | semidirect |
| 80. C3×C72 | C22×D4 | semidirect |
| 82. C2×C7×D4 | C3×D7 | semidirect |
| 88. C2×C72 | C2×C3×D4 | semidirect |
| 91. C7⋊D7 | C2×C3×D4 | direct (N × H) |
| 95. C22×C3×C7 | C22×D7 | semidirect |
| 101. C3×C4×C7 | C22×D7 | semidirect |
| 103. C23×C7 | C2×C3×D7 | semidirect |
| 108. C7×D4 | C2×C3×D7 | semidirect |
| 109. C2×C4×C7 | C2×C3×D7 | semidirect |
| 114. C72 | C22×C3×D4 | semidirect |
| 119. C2×C3×D4 | C7⋊D7 | direct (N × H) |
| 122. C2×C3×C7 | D4×D7 | semidirect |
| 129. C22×C7 | C22×C3×D7 | semidirect |
| 135. C4×C7 | C22×C3×D7 | semidirect |
| 141. C23×C3 | C2×C7⋊D7 | semidirect |
| 144. C3×D4 | C2×C7⋊D7 | direct (N × H) |
| 147. C2×C3×C4 | C2×C7⋊D7 | semidirect |
| 148. C3×C7 | C2×D4×D7 | semidirect |
| 153. C2×D4 | C3×C7⋊D7 | direct (N × H) |
| 156. C2×C7 | C3×D4×D7 | semidirect |
| 167. C22×C3 | C22×C7⋊D7 | semidirect |
| 169. C3×C4 | C22×C7⋊D7 | semidirect |
| 174. C23 | C2×C3×C7⋊D7 | semidirect |
| 177. D4 | C2×C3×C7⋊D7 | direct (N × H) |
| 180. C2×C4 | C2×C3×C7⋊D7 | semidirect |
| 181. C7 | C2×C3×D4×D7 | semidirect |
| 185. C2×C3 | D4×C7⋊D7 | direct (N × H) |
| 194. C22 | C22×C3×C7⋊D7 | semidirect |
| 196. C4 | C22×C3×C7⋊D7 | semidirect |
| 197. C3 | C2×D4×C7⋊D7 | direct (N × H) |
| 201. C2 | C3×D4×C7⋊D7 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C22⋊(C7⋊D7) | 2 |
| C23×C3×C7⋊D7 | 2 |
| C2×C3×C4⋊(C7⋊D7) | 2 |
| C2×C3×C72×D4 | 2 |
| C3×D4×C7⋊D7 | 2 |
| C2×C3×C4×C7⋊D7 | 2 |
| C2×D4×C7⋊D7 | 3 |
| C2×C3×D4×D7 | 7 |