Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
984 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 984 conjugacy classes of subgroups — too many to draw. Only its 210 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 |
|---|---|---|
| 2. C33×C4×C9 | C2 | semidirect |
| 3. C32×C3⋊Dic9 | C2 | semidirect |
| 5. C3×C4×C3⋊D9 | C3 | direct (N × H) |
| 8. C32×C3⋊D9 | C4 | direct (N × H) |
| 16. C32×C4×C9 | D3 | semidirect |
| 17. C32×C4×C9 | C2×C3 | semidirect |
| 18. C3×C3⋊Dic9 | C2×C3 | semidirect |
| 20. C33×C9 | C2×C4 | semidirect |
| 24. C4×C3⋊D9 | C32 | direct (N × H) |
| 32. C3×C3⋊D9 | C3×C4 | direct (N × H) |
| 39. C33×C4 | D9 | semidirect |
| 51. C3×C4×C9 | C3×D3 | semidirect |
| 52. C3×C4×C9 | C2×C32 | semidirect |
| 53. C3⋊Dic9 | C2×C32 | semidirect |
| 58. C32×C9 | C4×D3 | semidirect |
| 59. C32×C9 | C2×C3×C4 | semidirect |
| 79. C3⋊D9 | C32×C4 | direct (N × H) |
| 91. C32×C4 | C3×D9 | semidirect |
| 92. C32×C4 | C3⋊D9 | direct (N × H) |
| 100. C4×C9 | C32×D3 | semidirect |
| 104. C33 | C4×D9 | semidirect |
| 111. C3×C9 | C3×C4×D3 | semidirect |
| 112. C3×C9 | C2×C32×C4 | semidirect |
| 138. C3×C4 | C32×D9 | semidirect |
| 139. C3×C4 | C3×C3⋊D9 | direct (N × H) |
| 148. C32 | C3×C4×D9 | semidirect |
| 149. C32 | C4×C3⋊D9 | direct (N × H) |
| 153. C9 | C32×C4×D3 | semidirect |
| 165. C4 | C32×C3⋊D9 | direct (N × H) |
| 168. C3 | C32×C4×D9 | semidirect |
| 169. C3 | C3×C4×C3⋊D9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C3⋊D9 | 2 |
| C33×C4×C9 | 2 |
| C32×C3⋊Dic9 | 2 |
| C32×C4×C3⋊D3 | 3 |
| C3×C4×C3⋊D9 | 3 |
| C32×C4×D9 | 3 |