Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
275 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 275 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #92297 |
| commutator, hypocenter | C32×C9 | C2×C9 |
| Frattini, socle | C33 | C3×C3⋊D3 |
| Fitting | C9×C32⋊C9 | C2 |
| prime radical | C3×C3⋊(C3⋊D9) | C3 |
| cosocle | C33×C9 | C2×C3 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C9×C32⋊C9 | C2 | semidirect |
| 10. C3×C92 | D3 | semidirect |
| 12. #6855 | D3 | semidirect |
| 14. C3⋊(C3⋊D9) | C9 | semidirect |
| 30. C32×C9 | C2×C9 | semidirect |
| 36. C32⋊C9 | D9 | semidirect |
| 85. C3×C9 | C3⋊D9 | semidirect |
| 109. C32 | C9×D9 | semidirect |
| 122. C9 | (C3⋊D3)⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×C32⋊C9 | 2 |
| C3×C3⋊(C3⋊D9) | 3 |
| C3⋊((C3⋊D3)⋊C9) | 3 |
| C9×C3⋊D9 | 3 |
| #92158 | 3 |