Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
278 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C3⋊AGL(1,ℤ/9) |
| commutator, hypocenter | C32⋊C9 | C2×C9 |
| Frattini, socle | C33 | C3×C3⋊D3 |
| Fitting | #10624556 | C2 |
| prime radical | C3×#4181 | C3 |
| cosocle | C3×C32⋊C9 | C2×C3 |
| LCS | G ▷ C32⋊C9 | |
| UCS | C1 ◁ C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10624556 | C2 | semidirect |
| 6. C3×C9⋊C9 | D3 | semidirect |
| 15. #4181 | C9 | semidirect |
| 29. C32⋊C9 | C2×C9 | semidirect |
| 64. C3×C9 | D3×C9 | semidirect |
| 88. C32 | D9⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624556 | 2 |
| C3×C9×C3⋊D3 | 3 |
| C3×#4181 | 3 |
| C3×D9⋊C9 | 3 |