Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
762 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 762 conjugacy classes of subgroups — too many to draw. Only its 232 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. C23×C3×D9 | C2 | semidirect |
| 2. C2×C3×D4×C9 | C2 | semidirect |
| 3. C2×C3×#611 | C2 | semidirect |
| 4. C3×D4×D9 | C2 | direct (N × H) |
| 5. C2×C3×D36 | C2 | semidirect |
| 6. C2×C3×C4×D9 | C2 | semidirect |
| 8. C2×D4×D9 | C3 | direct (N × H) |
| 9. C23×C3×C9 | C22 | semidirect |
| 12. C22×C3×D9 | C22 | semidirect |
| 13. C22×C3×D9 | C22 | semidirect |
| 14. C3×D4×C9 | C22 | semidirect |
| 15. C2×C3×C4×C9 | C22 | semidirect |
| 16. C3×#611 | C22 | semidirect |
| 17. C2×C3×Dic9 | C22 | semidirect |
| 18. C3×D36 | C22 | semidirect |
| 19. C3×C4×D9 | C22 | semidirect |
| 26. C23×D9 | C2×C3 | semidirect |
| 28. C2×D4×C9 | C2×C3 | semidirect |
| 29. C2×#611 | C2×C3 | semidirect |
| 30. D4×D9 | C2×C3 | direct (N × H) |
| 31. C2×D36 | C2×C3 | semidirect |
| 32. C2×C4×D9 | C2×C3 | semidirect |
| 35. C22×C3×C9 | C23 | semidirect |
| 38. C2×C3×D9 | D4 | direct (N × H) |
| 40. C2×C3×D9 | C23 | semidirect |
| 41. C3×C4×C9 | C23 | semidirect |
| 42. C3×Dic9 | C23 | semidirect |
| 57. C23×C9 | C22×C3 | semidirect |
| 60. C22×D9 | C22×C3 | semidirect |
| 61. C22×D9 | C22×C3 | semidirect |
| 63. D4×C9 | C22×C3 | semidirect |
| 65. C2×C4×C9 | C22×C3 | semidirect |
| 66. #611 | C22×C3 | semidirect |
| 67. C2×Dic9 | C22×C3 | semidirect |
| 68. D36 | C22×C3 | semidirect |
| 69. C4×D9 | C22×C3 | semidirect |
| 71. C2×C3×C9 | C2×D4 | semidirect |
| 74. C3×D9 | C2×D4 | direct (N × H) |
| 81. C2×C3×D4 | D9 | direct (N × H) |
| 103. C22×C9 | C23×C3 | semidirect |
| 106. C2×D9 | C3×D4 | direct (N × H) |
| 108. C2×D9 | C23×C3 | semidirect |
| 110. C4×C9 | C23×C3 | semidirect |
| 111. Dic9 | C23×C3 | semidirect |
| 113. C3×C9 | C22×D4 | semidirect |
| 119. C23×C3 | C2×D9 | semidirect |
| 128. C3×D4 | C2×D9 | direct (N × H) |
| 133. C2×C3×C4 | C2×D9 | semidirect |
| 148. C2×C9 | C2×C3×D4 | semidirect |
| 151. D9 | C2×C3×D4 | direct (N × H) |
| 156. C2×D4 | C3×D9 | direct (N × H) |
| 169. C22×C3 | C22×D9 | semidirect |
| 179. C3×C4 | C22×D9 | semidirect |
| 184. C9 | C22×C3×D4 | semidirect |
| 189. C23 | C2×C3×D9 | semidirect |
| 192. D4 | C2×C3×D9 | direct (N × H) |
| 195. C2×C4 | C2×C3×D9 | semidirect |
| 203. C2×C3 | D4×D9 | direct (N × H) |
| 216. C22 | C22×C3×D9 | semidirect |
| 218. C4 | C22×C3×D9 | semidirect |
| 220. C3 | C2×D4×D9 | direct (N × H) |
| 225. C2 | C3×D4×D9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×D9 | 2 |
| C2×C3×D4×C9 | 2 |
| C2×C3×#611 | 2 |
| C3×D4×D9 | 2 |
| C2×C3×D36 | 2 |
| C2×C3×C4×D9 | 2 |
| C2×C3×D3×D4 | 3 |
| C2×D4×D9 | 3 |