Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
19068 conjugacy classes of subgroups; only the 2531 normal subgroups are shown.
This group has 19068 conjugacy classes of subgroups — too many to draw. Only its 2531 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. C24×C3⋊(C3⋊D3) | C2 | semidirect |
| 2. C22×C33×D4 | C2 | semidirect |
| 3. C22×#6312 | C2 | semidirect |
| 4. C2×D4×C3⋊(C3⋊D3) | C2 | direct (N × H) |
| 5. C22×C4⋊(C3⋊(C3⋊D3)) | C2 | semidirect |
| 6. C22×C4×C3⋊(C3⋊D3) | C2 | semidirect |
| 8. C24×C33 | C22 | semidirect |
| 11. C23×C3⋊(C3⋊D3) | C22 | semidirect |
| 12. C23×C3⋊(C3⋊D3) | C22 | semidirect |
| 13. C2×C33×D4 | C22 | semidirect |
| 14. C22×C33×C4 | C22 | semidirect |
| 15. C2×#6312 | C22 | semidirect |
| 16. C22×C3⋊(C3⋊Dic3) | C22 | semidirect |
| 17. D4×C3⋊(C3⋊D3) | C22 | direct (N × H) |
| 18. C2×C4⋊(C3⋊(C3⋊D3)) | C22 | semidirect |
| 19. C2×C4×C3⋊(C3⋊D3) | C22 | semidirect |
| 21. C22×C32×D4 | D3 | semidirect |
| 28. C23×C33 | C23 | semidirect |
| 31. C22×C3⋊(C3⋊D3) | D4 | direct (N × H) |
| 33. C22×C3⋊(C3⋊D3) | C23 | semidirect |
| 34. C22×C3⋊(C3⋊D3) | C23 | semidirect |
| 35. C33×D4 | C23 | semidirect |
| 36. C2×C33×C4 | C23 | semidirect |
| 37. #6312 | C23 | semidirect |
| 38. C2×C3⋊(C3⋊Dic3) | C23 | semidirect |
| 39. C4⋊(C3⋊(C3⋊D3)) | C23 | semidirect |
| 40. C4×C3⋊(C3⋊D3) | C23 | semidirect |
| 42. C24×C32 | C2×D3 | semidirect |
| 47. C2×C32×D4 | C2×D3 | semidirect |
| 48. C22×C32×C4 | C2×D3 | semidirect |
| 55. C22×C33 | C2×D4 | semidirect |
| 57. C22×C33 | C24 | semidirect |
| 60. C2×C3⋊(C3⋊D3) | C2×D4 | direct (N × H) |
| 62. C2×C3⋊(C3⋊D3) | C24 | semidirect |
| 63. C33×C4 | C24 | semidirect |
| 64. C3⋊(C3⋊Dic3) | C24 | semidirect |
| 66. C22×C3×D4 | C3⋊D3 | semidirect |
| 73. C23×C32 | C22×D3 | semidirect |
| 80. C32×D4 | C22×D3 | semidirect |
| 81. C2×C32×C4 | C22×D3 | semidirect |
| 88. C2×C33 | C22×D4 | semidirect |
| 91. C3⋊(C3⋊D3) | C22×D4 | direct (N × H) |
| 92. C24×C3 | C2×C3⋊D3 | semidirect |
| 97. C2×C3×D4 | C2×C3⋊D3 | semidirect |
| 98. C22×C3×C4 | C2×C3⋊D3 | semidirect |
| 105. C22×C32 | D3×D4 | semidirect |
| 107. C22×C32 | C23×D3 | semidirect |
| 113. C32×C4 | C23×D3 | semidirect |
| 119. C22×D4 | C3⋊(C3⋊D3) | direct (N × H) |
| 121. C33 | C23×D4 | semidirect |
| 124. C23×C3 | C22×C3⋊D3 | semidirect |
| 131. C3×D4 | C22×C3⋊D3 | semidirect |
| 132. C2×C3×C4 | C22×C3⋊D3 | semidirect |
| 138. C2×C32 | C2×D3×D4 | semidirect |
| 146. C24 | C2×C3⋊(C3⋊D3) | semidirect |
| 150. C2×D4 | C2×C3⋊(C3⋊D3) | direct (N × H) |
| 153. C22×C4 | C2×C3⋊(C3⋊D3) | semidirect |
| 155. C22×C3 | D4×C3⋊D3 | semidirect |
| 157. C22×C3 | C23×C3⋊D3 | semidirect |
| 163. C3×C4 | C23×C3⋊D3 | semidirect |
| 165. C32 | C22×D3×D4 | semidirect |
| 174. C23 | C22×C3⋊(C3⋊D3) | semidirect |
| 177. D4 | C22×C3⋊(C3⋊D3) | direct (N × H) |
| 180. C2×C4 | C22×C3⋊(C3⋊D3) | semidirect |
| 182. C2×C3 | C2×D4×C3⋊D3 | semidirect |
| 192. C22 | D4×C3⋊(C3⋊D3) | direct (N × H) |
| 194. C22 | C23×C3⋊(C3⋊D3) | semidirect |
| 196. C4 | C23×C3⋊(C3⋊D3) | semidirect |
| 197. C3 | C22×D4×C3⋊D3 | semidirect |
| 201. C2 | C2×D4×C3⋊(C3⋊D3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C3⋊(C3⋊D3) | 2 |
| C22×C33×D4 | 2 |
| C22×#6312 | 2 |
| C2×D4×C3⋊(C3⋊D3) | 2 |
| C22×C4⋊(C3⋊(C3⋊D3)) | 2 |
| C22×C4×C3⋊(C3⋊D3) | 2 |
| C22×D4×C3⋊D3 | 3 |