Finite Group DatabasebetaFinite Group DatabasebetaOrder 2916.
622 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 622 conjugacy classes of subgroups — too many to draw. Only its 80 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. C3⋊(C3⋊(D9⋊C9)) | C2 | semidirect |
| 2. C32×D9⋊C9 | C2 | semidirect |
| 3. C3⋊D3×C9⋊C9 | C2 | semidirect |
| 7. C32×C9⋊C9 | C22 | semidirect |
| 19. C3×D9⋊C9 | D3 | semidirect |
| 22. D9×C3⋊D3 | C9 | semidirect |
| 32. C3×C9⋊C9 | C2×D3 | semidirect |
| 37. C3⋊(C3⋊D9) | C2×C9 | semidirect |
| 44. C9×C3⋊D3 | C2×C9 | semidirect |
| 53. C32×D9 | C2×C9 | semidirect |
| 59. D9⋊C9 | C3⋊D3 | direct (N × H) |
| 79. C32×C9 | C22×C9 | semidirect |
| 86. C9⋊C9 | C2×C3⋊D3 | semidirect |
| 118. C3×D9 | D3×C9 | semidirect |
| 151. C3×C9 | C2×D3×C9 | semidirect |
| 161. C3⋊D3 | D9⋊C9 | direct (N × H) |
| 180. D9 | C9×C3⋊D3 | semidirect |
| 192. C32 | C2×D9⋊C9 | semidirect |
| 203. C9 | C2×C9×C3⋊D3 | semidirect |
| 221. C3 | D3×D9⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊(C3⋊(D9⋊C9)) | 2 |
| C32×D9⋊C9 | 2 |
| C3⋊D3×C9⋊C9 | 2 |
| D3×C9×C3⋊D3 | 3 |
| C3×D9×C3⋊D3 | 3 |
| D3×D9⋊C9 | 3 |