Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
145 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 145 conjugacy classes of subgroups — too many to draw. Only its 28 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. #10624795 | C2 | semidirect |
| 2. C9×#272 | C3 | semidirect |
| 5. #272⋊C9 | C3 | semidirect |
| 6. #272⋊C9 | C3 | semidirect |
| 10. C3×C9⋊C9 | D3 | semidirect |
| 48. #272 | 3−1+2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624795 | 2 |
| C9×#272 | 3 |
| C3×#4178 | 3 |
| D3×C9⋊C9 | 3 |
| #272⋊C9 | 3 |