Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
791 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 791 conjugacy classes of subgroups — too many to draw. Only its 180 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. C32×C9×A4 | C2 | semidirect |
| 3. C22×C3×D3×C9 | C3 | semidirect |
| 5. C3×D3×C22⋊C9 | C3 | semidirect |
| 6. D3×C9×A4 | C3 | direct (N × H) |
| 9. C22×C32×C9 | C2×C3 | semidirect |
| 12. C32×C22⋊C9 | C2×C3 | semidirect |
| 17. C3×C9×A4 | D3 | direct (N × H) |
| 18. C3×C9×A4 | C2×C3 | semidirect |
| 22. C3×D3×A4 | C9 | direct (N × H) |
| 25. C22×D3×C9 | C32 | semidirect |
| 28. D3×C22⋊C9 | C32 | semidirect |
| 35. C3×D3×C9 | A4 | direct (N × H) |
| 42. C32×A4 | C2×C9 | semidirect |
| 49. C22×C3×C9 | C3×D3 | semidirect |
| 50. C22×C3×C9 | C2×C32 | semidirect |
| 55. C3×C22⋊C9 | C3×D3 | semidirect |
| 56. C3×C22⋊C9 | C2×C32 | semidirect |
| 60. C9×A4 | C3×D3 | direct (N × H) |
| 69. C32×C9 | C2×A4 | semidirect |
| 71. C22×C3×D3 | C3×C9 | semidirect |
| 75. D3×A4 | C3×C9 | direct (N × H) |
| 94. D3×C9 | C3×A4 | direct (N × H) |
| 99. C22×C32 | C2×C3×C9 | semidirect |
| 110. C3×A4 | D3×C9 | direct (N × H) |
| 111. C3×A4 | C2×C3×C9 | semidirect |
| 116. C22×C9 | C32×D3 | semidirect |
| 118. C22⋊C9 | C32×D3 | semidirect |
| 136. C3×C9 | D3×A4 | direct (N × H) |
| 137. C3×C9 | C2×C3×A4 | semidirect |
| 140. C22×D3 | C32×C9 | semidirect |
| 154. C3×D3 | C9×A4 | direct (N × H) |
| 167. C22×C3 | C3×D3×C9 | semidirect |
| 168. C22×C3 | C2×C32×C9 | semidirect |
| 173. A4 | C3×D3×C9 | direct (N × H) |
| 183. C32 | C2×C9×A4 | semidirect |
| 189. C9 | C3×D3×A4 | direct (N × H) |
| 202. D3 | C3×C9×A4 | direct (N × H) |
| 205. C22 | C32×D3×C9 | semidirect |
| 210. C3 | D3×C9×A4 | direct (N × H) |
| 211. C3 | C2×C3×C9×A4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C9×A4 | 2 |
| C32×D3×A4 | 3 |
| C22×C3×D3×C9 | 3 |
| C2×C3×C9×A4 | 3 |
| C3×D3×C22⋊C9 | 3 |
| D3×C9×A4 | 3 |
| C32×D3×C9 | 4 |