Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
456 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 141 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. C32×Q8×C9 | C2 | semidirect |
| 2. C9×C4⋊(C3⋊D3) | C2 | semidirect |
| 3. C4×C9×C3⋊D3 | C2 | semidirect |
| 13. C3×Q8×C9 | D3 | semidirect |
| 18. #3832 | C9 | direct (N × H) |
| 28. C32×C9 | #41 | semidirect |
| 30. C32×Q8 | C2×C9 | semidirect |
| 32. C4⋊(C3⋊D3) | C2×C9 | semidirect |
| 33. C4×C3⋊D3 | C2×C9 | semidirect |
| 37. Q8×C9 | C3⋊D3 | semidirect |
| 60. C3×C9 | #239 | semidirect |
| 62. C3×Q8 | D3×C9 | semidirect |
| 85. C32 | C9×#41 | semidirect |
| 88. C9 | #3832 | direct (N × H) |
| 89. Q8 | C9×C3⋊D3 | semidirect |
| 101. C3 | C9×#239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×Q8×C9 | 2 |
| C9×C4⋊(C3⋊D3) | 2 |
| C4×C9×C3⋊D3 | 2 |
| C3×#3832 | 3 |
| C9×#239 | 3 |