Finite Group DatabasebetaFinite Group DatabasebetaOrder 2916.
1098 conjugacy classes of subgroups; only the 315 normal subgroups are shown.
This group has 1098 conjugacy classes of subgroups — too many to draw. Only its 315 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. D3×#6900 | C2 | direct (N × H) |
| 2. C2×C3×#6900 | C2 | semidirect |
| 5. C2×D3×C9⋊C9 | C3 | semidirect |
| 6. C2×D3×C92 | C3 | semidirect |
| 7. C3×#6900 | C22 | semidirect |
| 14. C2×#6900 | D3 | direct (N × H) |
| 15. C2×C3×C9⋊C9 | C2×C3 | semidirect |
| 16. C2×C3×C92 | C2×C3 | semidirect |
| 17. D3×C9⋊C9 | C2×C3 | semidirect |
| 18. D3×C92 | C2×C3 | semidirect |
| 30. #6900 | C2×D3 | direct (N × H) |
| 31. C3×C9⋊C9 | C22×C3 | semidirect |
| 32. C3×C92 | C22×C3 | semidirect |
| 50. C2×C9⋊C9 | C3×D3 | semidirect |
| 53. C2×C92 | C3×D3 | semidirect |
| 61. C2×D3×C9 | 3−1+2 | semidirect |
| 73. C9⋊C9 | C2×C3×D3 | semidirect |
| 75. C92 | C2×C3×D3 | semidirect |
| 96. C2×C3×C9 | C2×3−1+2 | semidirect |
| 100. D3×C9 | C2×3−1+2 | semidirect |
| 121. C3×C9 | C22×3−1+2 | semidirect |
| 140. C2×C9 | D3×3−1+2 | semidirect |
| 143. C2×D3 | #6900 | direct (N × H) |
| 154. C9 | C2×D3×3−1+2 | semidirect |
| 160. C2×C3 | C2×#6900 | semidirect |
| 162. D3 | C2×#6900 | direct (N × H) |
| 167. C3 | C22×#6900 | semidirect |
| 170. C2 | D3×#6900 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×#6900 | 2 |
| C2×C3×#6900 | 2 |
| C2×C3×D3×3−1+2 | 3 |
| C22×#6900 | 3 |
| C2×D3×C9⋊C9 | 3 |
| C2×D3×C92 | 3 |