Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
181 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 181 conjugacy classes of subgroups — too many to draw. Only its 36 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×#6204 | C2 | semidirect |
| 4. C3⋊(#41⋊C9) | C3 | semidirect |
| 11. #6204 | D3 | semidirect |
| 12. C3×Q8⋊C9 | C2×C3 | semidirect |
| 36. Q8⋊C9 | C3×D3 | semidirect |
| 45. #239 | 3−1+2 | semidirect |
| 120. C3 | #88691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6204 | 2 |
| C32×#239 | 3 |
| #88691 | 3 |
| C3⋊(#41⋊C9) | 3 |
| Dic3×3−1+2 | 4 |