Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
256 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 81 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. Q8×C32⋊C9 | C2 | semidirect |
| 2. C4⋊((C3⋊D3)⋊C9) | C2 | semidirect |
| 3. C4×(C3⋊D3)⋊C9 | C2 | semidirect |
| 13. C3×Q8×C9 | D3 | semidirect |
| 18. #3832 | C9 | semidirect |
| 29. C32⋊C9 | #41 | semidirect |
| 33. C32×Q8 | C2×C9 | semidirect |
| 35. C4⋊(C3⋊D3) | C2×C9 | semidirect |
| 36. C4×C3⋊D3 | C2×C9 | semidirect |
| 70. C3×C9 | #239 | semidirect |
| 108. C32 | C9×#41 | semidirect |
| 112. Q8 | (C3⋊D3)⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C32⋊C9 | 2 |
| C4⋊((C3⋊D3)⋊C9) | 2 |
| C4×(C3⋊D3)⋊C9 | 2 |
| C3×#3832 | 3 |
| C9×#239 | 3 |