Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
123 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 123 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. #10624793 | C2 | semidirect |
| 3. #6894⋊C2 | C3 | semidirect |
| 5. C3×D9⋊C9 | C3 | semidirect |
| 7. #6894 | C2×C3 | semidirect |
| 9. C3×C9⋊C9 | C2×C3 | semidirect |
| 74. D9 | #731 | semidirect |
| 91. C9 | C2×#731 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624793 | 2 |
| D3×#731 | 3 |
| #6894⋊C2 | 3 |
| D9×H(3,𝔽3) | 3 |
| C3×D9⋊C9 | 3 |