Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
450 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 128 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. C3×C4×C32⋊C9 | C2 | semidirect |
| 3. C3×(C3⋊Dic3)⋊C9 | C2 | semidirect |
| 6. C4×(C3⋊D3)⋊C9 | C3 | direct (N × H) |
| 8. C3×(C3⋊D3)⋊C9 | C4 | direct (N × H) |
| 14. C32×C4×C9 | D3 | semidirect |
| 18. C4×C32⋊C9 | C2×C3 | semidirect |
| 19. (C3⋊Dic3)⋊C9 | C2×C3 | semidirect |
| 20. C3×C32⋊C9 | C2×C4 | semidirect |
| 21. C3×C4×C3⋊D3 | C9 | semidirect |
| 34. (C3⋊D3)⋊C9 | C3×C4 | direct (N × H) |
| 44. C33×C4 | C2×C9 | semidirect |
| 47. C3×C3⋊Dic3 | C2×C9 | semidirect |
| 59. C3×C4×C9 | C3×D3 | semidirect |
| 63. C32×C9 | C4×D3 | semidirect |
| 65. C32⋊C9 | C2×C3×C4 | semidirect |
| 67. C4×C3⋊D3 | C3×C9 | semidirect |
| 81. C3×C3⋊D3 | C4×C9 | semidirect |
| 114. C32×C4 | C2×C3×C9 | semidirect |
| 116. C3⋊Dic3 | C2×C3×C9 | semidirect |
| 130. C33 | C2×C4×C9 | semidirect |
| 138. C3×C9 | C3×C4×D3 | semidirect |
| 160. C3⋊D3 | C3×C4×C9 | semidirect |
| 179. C3×C4 | (C3⋊D3)⋊C9 | direct (N × H) |
| 198. C32 | C2×C3×C4×C9 | semidirect |
| 217. C4 | C3×(C3⋊D3)⋊C9 | direct (N × H) |
| 223. C3 | C4×(C3⋊D3)⋊C9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×(C3⋊D3)⋊C9 | 2 |
| C3×C4×C32⋊C9 | 2 |
| C3×(C3⋊Dic3)⋊C9 | 2 |
| C32×C4×C3⋊D3 | 3 |
| C3×C4×D3×C9 | 3 |
| C4×(C3⋊D3)⋊C9 | 3 |