Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
488 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 89 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×C3⋊(C3⋊Dic9) | C2 | semidirect |
| 2. C9×#638 | C2 | semidirect |
| 3. C32×#611 | C2 | semidirect |
| 4. #10619877 | C2 | semidirect |
| 5. C3⋊D3×Dic9 | C2 | semidirect |
| 6. D9×C3⋊Dic3 | C2 | semidirect |
| 7. #10619867 | C2 | semidirect |
| 27. C3×#611 | D3 | semidirect |
| 56. C32×C9 | #41 | semidirect |
| 59. #638 | D9 | semidirect |
| 74. #611 | C3⋊D3 | semidirect |
| 121. C3×C9 | #237 | semidirect |
| 172. C32 | #3699 | semidirect |
| 175. C9 | #3830 | semidirect |
| 201. C3 | #88663 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3⋊(C3⋊Dic9) | 2 |
| C9×#638 | 2 |
| C32×#611 | 2 |
| #10619877 | 2 |
| C3⋊D3×Dic9 | 2 |
| D9×C3⋊Dic3 | 2 |
| #10619867 | 2 |
| #89029 | 3 |
| #88663 | 3 |