Finite Group DatabasebetaFinite Group Databasebeta← (C3×(C3⋊D3)⋊C3)⋊C9 #13090637
Order 1458.
329 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 329 conjugacy classes of subgroups — too many to draw. Only its 49 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. #10624555 | C2 | semidirect |
| 2. C3×C9×C3⋊D3 | C3 | semidirect |
| 5. C3×(C3⋊D3)⋊C9 | C3 | semidirect |
| 7. C33×C9 | C2×C3 | semidirect |
| 11. C3×C32⋊C9 | D3 | semidirect |
| 12. C3×C32⋊C9 | C2×C3 | semidirect |
| 18. C3×(C3⋊D3)⋊C3 | C9 | semidirect |
| 32. C3×H(3,𝔽3) | C2×C9 | semidirect |
| 85. C33 | D3×C9 | semidirect |
| 113. C3×C9 | (C3⋊D3)⋊C3 | semidirect |
| 118. C3⋊D3 | C32⋊C9 | semidirect |
| 160. C32 | C2×C32⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624555 | 2 |
| C3×C9×C3⋊D3 | 3 |
| C32×(C3⋊D3)⋊C3 | 3 |
| D3×C32⋊C9 | 3 |
| C3×(C3⋊D3)⋊C9 | 3 |