Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
308 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C3 | C3×#4207 |
| commutator, cosocle, hypocenter | C32⋊C9 | C2×C32 |
| Frattini, socle | C32 | C32×C3⋊D3 |
| Fitting | #10624888 | C2 |
| hypercenter | C32 | #4207 |
| LCS | G ▷ C32⋊C9 | |
| UCS | C1 ◁ C3 ◁ C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10624888 | C2 | semidirect |
| 2. #92304 | C3 | semidirect |
| 3. C3×#4181 | C3 | semidirect |
| 8. #6893 | C2×C3 | semidirect |
| 12. C9⋊H(3,𝔽3) | D3 | semidirect |
| 16. C9×H(3,𝔽3) | D3 | semidirect |
| 17. C3×C32⋊C9 | C2×C3 | semidirect |
| 29. C3×3−1+2 | C3×D3 | semidirect |
| 37. C32×C9 | C3×D3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624888 | 2 |
| #92304 | 3 |
| C3×#4181 | 3 |
| D9⋊H(3,𝔽3) | 3 |
| (C3⋊D3)⋊H(3,𝔽3) | 3 |
| D9×H(3,𝔽3) | 3 |