Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
212 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | #4169 |
| commutator, cosocle, hypocenter | C32⋊C9 | C2×C32 |
| Frattini | C33 | C32×D3 |
| Fitting | #10624688 | C2 |
| socle | C32 | C3×(C3⋊D3)⋊C3 |
| prime radical | #92174 | C3 |
| LCS | G ▷ C32⋊C9 | |
| UCS | C1 ◁ C9 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10624688 | C2 | semidirect |
| 3. #92295 | C3 | semidirect |
| 4. #92178 | C3 | semidirect |
| 5. #92176 | C3 | semidirect |
| 9. #6887 | C2×C3 | semidirect |
| 11. #6868 | C2×C3 | semidirect |
| 13. #6867 | C2×C3 | semidirect |
| 34. C32×C9 | D9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624688 | 2 |
| C3×C9×C3⋊D3 | 3 |
| #92295 | 3 |
| #92178 | 3 |
| #92176 | 3 |
| #92174 | 3 |