Finite Group DatabasebetaFinite Group DatabasebetaOrder 2916.
569 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 569 conjugacy classes of subgroups — too many to draw. Only its 104 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. #4169⋊C9 | C2 | direct (N × H) |
| 2. C2×#10624556 | C2 | semidirect |
| 4. C2×C3⋊(D9⋊C9) | C3 | semidirect |
| 6. C2×#92158 | C3 | semidirect |
| 7. C2×#92158 | C3 | semidirect |
| 8. #10624556 | C22 | semidirect |
| 12. C2×C3×C9⋊C9 | C2×C3 | semidirect |
| 15. C3⋊(D9⋊C9) | C2×C3 | semidirect |
| 19. C2×#6855 | C2×C3 | semidirect |
| 20. C2×#6855 | C2×C3 | semidirect |
| 21. #92158 | C2×C3 | semidirect |
| 22. #92158 | C2×C3 | semidirect |
| 33. C2×#4169 | C9 | semidirect |
| 34. C2×#4169 | C9 | semidirect |
| 35. C2×#4169 | C9 | semidirect |
| 38. C3×C9⋊C9 | C22×C3 | semidirect |
| 43. #6855 | C22×C3 | semidirect |
| 44. #6855 | C22×C3 | semidirect |
| 81. C2×C32⋊C9 | C2×C9 | semidirect |
| 82. C2×C32⋊C9 | C2×C9 | semidirect |
| 83. C2×C32⋊C9 | C2×C9 | semidirect |
| 85. #4169 | C2×C9 | semidirect |
| 86. #4169 | C2×C9 | semidirect |
| 87. #4169 | C2×C9 | semidirect |
| 97. C2×C3⋊D9 | C3×C9 | semidirect |
| 138. C32⋊C9 | C22×C9 | semidirect |
| 139. C32⋊C9 | C22×C9 | semidirect |
| 140. C32⋊C9 | C22×C9 | semidirect |
| 212. C2×C3×C9 | C2×C3×C9 | semidirect |
| 213. C3⋊D9 | C2×C3×C9 | semidirect |
| 311. C3×C9 | C22×C3×C9 | semidirect |
| 342. C2×C32 | D9⋊C9 | semidirect |
| 343. C2×C32 | D9⋊C9 | semidirect |
| 344. C2×C32 | D9⋊C9 | semidirect |
| 422. C32 | C2×D9⋊C9 | semidirect |
| 423. C32 | C2×D9⋊C9 | semidirect |
| 424. C32 | C2×D9⋊C9 | semidirect |
| 484. C2 | #4169⋊C9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #4169⋊C9 | 2 |
| C2×#10624556 | 2 |
| C2×C3×C9×C3⋊D3 | 3 |
| C2×C3⋊(D9⋊C9) | 3 |
| C2×C3×#4169 | 3 |
| C2×#92158 | 3 |