Finite Group DatabasebetaFinite Group Databasebeta← C9×C3⋊((C3⋊D3)⋊C3) #13091356
Order 1458.
599 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 599 conjugacy classes of subgroups — too many to draw. Only its 82 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. C3×C9×H(3,𝔽3) | C2 | semidirect |
| 2. C9×C3⋊(C3⋊D3) | C3 | semidirect |
| 5. C3⋊((C3⋊D3)⋊C9) | C3 | semidirect |
| 9. C33×C9 | D3 | semidirect |
| 10. C33×C9 | C2×C3 | semidirect |
| 14. C9×H(3,𝔽3) | D3 | semidirect |
| 17. C3×C32⋊C9 | C2×C3 | semidirect |
| 20. C3⋊((C3⋊D3)⋊C3) | C9 | direct (N × H) |
| 35. C3×H(3,𝔽3) | C2×C9 | semidirect |
| 53. C32×C9 | C3×D3 | semidirect |
| 54. C32×C9 | C3⋊D3 | semidirect |
| 60. C32⋊C9 | C3×D3 | semidirect |
| 61. C3⋊(C3⋊D3) | C3×C9 | semidirect |
| 88. C33 | D3×C9 | semidirect |
| 89. C33 | C2×C3×C9 | semidirect |
| 96. H(3,𝔽3) | D3×C9 | semidirect |
| 117. C3×C9 | (C3⋊D3)⋊C3 | semidirect |
| 152. C32 | C3×D3×C9 | semidirect |
| 154. C32 | C9×C3⋊D3 | semidirect |
| 162. C9 | C3⋊((C3⋊D3)⋊C3) | direct (N × H) |
| 175. C3 | C9×(C3⋊D3)⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×H(3,𝔽3) | 2 |
| C9×C3⋊(C3⋊D3) | 3 |
| C3×C3⋊((C3⋊D3)⋊C3) | 3 |
| C3×C9×C3⋊D3 | 3 |
| C3⋊((C3⋊D3)⋊C9) | 3 |
| C9×(C3⋊D3)⋊C3 | 3 |