Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
458 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 55 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 | C3⋊((C3⋊D3)⋊C3) |
| commutator, cosocle, hypocenter | C3×H(3,𝔽3) | C2×C32 |
| Frattini, socle | C32 | C32×C3⋊D3 |
| Fitting | #10624869 | C2 |
| prime radical | #92300 | C3 |
| LCS | G ▷ C3×H(3,𝔽3) | |
| UCS | C1 ◁ C9 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10624869 | C2 | semidirect |
| 2. C3⋊#4208 | C3 | semidirect |
| 4. #92305 | C3 | semidirect |
| 8. C3×#737 | C2×C3 | semidirect |
| 9. C33×C9 | D3 | semidirect |
| 11. #6893 | C2×C3 | semidirect |
| 17. C9×H(3,𝔽3) | D3 | semidirect |
| 49. C32×C9 | C3×D3 | semidirect |
| 56. C32⋊C9 | C3×D3 | semidirect |
| 102. C3×C9 | (C3⋊D3)⋊C3 | semidirect |
| 132. C32 | #4208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624869 | 2 |
| C3⋊#4208 | 3 |
| C3×C9×C3⋊D3 | 3 |
| #92305 | 3 |
| #92300 | 3 |
| C9×(C3⋊D3)⋊C3 | 3 |