Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
928 conjugacy classes of subgroups; only the 294 normal subgroups are shown.
This group has 928 conjugacy classes of subgroups — too many to draw. Only its 294 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 |
|---|---|---|
| 2. C2×C32×C4×D3 | C2 | semidirect |
| 3. C33×C22⋊C4 | C2 | semidirect |
| 4. C32×#217 | C2 | semidirect |
| 5. C32×(C2×D3)⋊C4 | C2 | semidirect |
| 7. C3×D3×C22⋊C4 | C3 | direct (N × H) |
| 10. C22×C32×D3 | C4 | semidirect |
| 13. C2×C33×C4 | C22 | semidirect |
| 14. C2×C32×Dic3 | C22 | semidirect |
| 19. C2×C3×C4×D3 | C2×C3 | semidirect |
| 23. C32×C22⋊C4 | D3 | direct (N × H) |
| 24. C32×C22⋊C4 | C2×C3 | semidirect |
| 25. C3×#217 | C2×C3 | semidirect |
| 26. C3×(C2×D3)⋊C4 | C2×C3 | semidirect |
| 28. C22×C33 | C2×C4 | semidirect |
| 33. C2×C32×D3 | C2×C4 | semidirect |
| 38. D3×C22⋊C4 | C32 | direct (N × H) |
| 47. C22×C3×D3 | C3×C4 | semidirect |
| 53. C2×C32×C4 | C2×D3 | semidirect |
| 54. C2×C32×C4 | C22×C3 | semidirect |
| 55. C2×C3×Dic3 | C22×C3 | semidirect |
| 61. C32×D3 | C22⋊C4 | direct (N × H) |
| 65. C2×C4×D3 | C2×C32 | semidirect |
| 69. C3×C22⋊C4 | C3×D3 | direct (N × H) |
| 70. C3×C22⋊C4 | C2×C32 | semidirect |
| 71. #217 | C2×C32 | semidirect |
| 72. (C2×D3)⋊C4 | C2×C32 | semidirect |
| 83. C22×C32 | C4×D3 | semidirect |
| 84. C22×C32 | C2×C3×C4 | semidirect |
| 90. C2×C3×D3 | C2×C3×C4 | semidirect |
| 98. C33 | C2×C22⋊C4 | semidirect |
| 107. C22×D3 | C32×C4 | semidirect |
| 113. C2×C3×C4 | C2×C3×D3 | semidirect |
| 114. C2×C3×C4 | C22×C32 | semidirect |
| 115. C2×Dic3 | C22×C32 | semidirect |
| 129. C3×D3 | C3×C22⋊C4 | direct (N × H) |
| 134. C22⋊C4 | C32×D3 | direct (N × H) |
| 145. C22×C3 | C3×C4×D3 | semidirect |
| 146. C22×C3 | C2×C32×C4 | semidirect |
| 152. C2×D3 | C2×C32×C4 | semidirect |
| 160. C32 | D3×C22⋊C4 | direct (N × H) |
| 161. C32 | C2×C3×C22⋊C4 | semidirect |
| 169. C2×C4 | C2×C32×D3 | semidirect |
| 182. D3 | C32×C22⋊C4 | direct (N × H) |
| 189. C22 | C32×C4×D3 | semidirect |
| 194. C3 | C3×D3×C22⋊C4 | direct (N × H) |
| 195. C3 | C2×C32×C22⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C32×D3 | 2 |
| C2×C32×C4×D3 | 2 |
| C33×C22⋊C4 | 2 |
| C32×#217 | 2 |
| C32×(C2×D3)⋊C4 | 2 |
| C2×C32×C22⋊C4 | 3 |
| C3×D3×C22⋊C4 | 3 |