Finite Group DatabasebetaFinite Group Databasebeta← C9×C4⋊((C3⋊D3)⋊C3) #14517299
Order 1944.
366 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×C9×(C3⋊D3)⋊C3 | C2 | semidirect |
| 2. C4×C9×H(3,𝔽3) | C2 | semidirect |
| 3. C9×C4⋊(C3⋊D3) | C3 | semidirect |
| 6. C4⋊((C3⋊D3)⋊C9) | C3 | semidirect |
| 9. C2×C9×C3⋊D3 | C2×C3 | semidirect |
| 14. C32×C4×C9 | D3 | semidirect |
| 15. C32×C4×C9 | C2×C3 | semidirect |
| 16. C2×(C3⋊D3)⋊C9 | C2×C3 | semidirect |
| 19. C4×C32⋊C9 | C2×C3 | semidirect |
| 20. C9×H(3,𝔽3) | D4 | semidirect |
| 24. C4⋊((C3⋊D3)⋊C3) | C9 | direct (N × H) |
| 45. C2×(C3⋊D3)⋊C3 | C2×C9 | semidirect |
| 50. C4×H(3,𝔽3) | C2×C9 | semidirect |
| 63. C32×C9 | D12 | semidirect |
| 64. C32×C9 | C3×D4 | semidirect |
| 67. C32⋊C9 | C3×D4 | semidirect |
| 69. C4⋊(C3⋊D3) | C3×C9 | semidirect |
| 98. C2×C3⋊D3 | C2×C3×C9 | semidirect |
| 110. C32×C4 | D3×C9 | semidirect |
| 111. C32×C4 | C2×C3×C9 | semidirect |
| 119. C4×C9 | (C3⋊D3)⋊C3 | semidirect |
| 124. H(3,𝔽3) | D4×C9 | semidirect |
| 181. C32 | C9×D12 | semidirect |
| 182. C32 | C3×D4×C9 | semidirect |
| 188. C9 | C4⋊((C3⋊D3)⋊C3) | direct (N × H) |
| 202. C4 | C9×(C3⋊D3)⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×(C3⋊D3)⋊C3 | 2 |
| C4×C9×H(3,𝔽3) | 2 |
| C9×C4⋊(C3⋊D3) | 3 |
| C3×C4⋊((C3⋊D3)⋊C3) | 3 |
| C3×C9×D12 | 3 |
| C4⋊((C3⋊D3)⋊C9) | 3 |