Finite Group DatabasebetaFinite Group DatabasebetaOrder 2916.
520 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 91 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. 3−1+2×C3⋊D9 | C2 | semidirect |
| 2. C3×D9×3−1+2 | C2 | semidirect |
| 3. D3×C9×3−1+2 | C2 | semidirect |
| 7. D3×C9×D9 | C3 | semidirect |
| 8. C3×C9×3−1+2 | C22 | semidirect |
| 16. C9×C3⋊D9 | C2×C3 | semidirect |
| 21. D9×3−1+2 | D3 | direct (N × H) |
| 24. D3×C92 | C2×C3 | semidirect |
| 25. C3×C9×D9 | C2×C3 | semidirect |
| 41. C9×3−1+2 | C2×D3 | semidirect |
| 44. C3×C92 | C22×C3 | semidirect |
| 62. D3×3−1+2 | D9 | direct (N × H) |
| 83. C9×D9 | C3×D3 | semidirect |
| 93. D3×D9 | 3−1+2 | direct (N × H) |
| 102. C3×3−1+2 | C2×D9 | semidirect |
| 126. C92 | C2×C3×D3 | semidirect |
| 158. C3⋊D9 | C2×3−1+2 | semidirect |
| 168. D3×C9 | C3×D9 | semidirect |
| 169. D3×C9 | C2×3−1+2 | semidirect |
| 177. C3×D9 | C2×3−1+2 | semidirect |
| 207. 3−1+2 | D3×D9 | direct (N × H) |
| 232. C3×C9 | C2×C3×D9 | semidirect |
| 233. C3×C9 | C22×3−1+2 | semidirect |
| 275. D9 | D3×3−1+2 | direct (N × H) |
| 313. C9 | C3×D3×D9 | semidirect |
| 314. C9 | C2×D3×3−1+2 | semidirect |
| 331. D3 | D9×3−1+2 | direct (N × H) |
| 341. C3 | C2×D9×3−1+2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| 3−1+2×C3⋊D9 | 2 |
| C3×D9×3−1+2 | 2 |
| D3×C9×3−1+2 | 2 |
| D32×3−1+2 | 3 |
| C32×D3×D9 | 3 |
| C2×D9×3−1+2 | 3 |
| D3×C9×D9 | 3 |