Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
341 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 341 conjugacy classes of subgroups — too many to draw. Only its 51 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 | #92391 |
| commutator, cosocle | C34 | C2×C32 |
| Frattini, socle | C32 | C32×C3⋊D3 |
| Fitting | #10624883 | C2 |
| prime radical | C3×C3⋊((C3⋊D3)⋊C3) | C3 |
| hypocenter | C33 | C2×3−1+2 |
| LCS | G ▷ C34 ▷ C33 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10624883 | C2 | semidirect |
| 3. C3⋊((C3⋊D3)⋊C9) | C3 | semidirect |
| 10. C9⋊H(3,𝔽3) | D3 | semidirect |
| 13. #6891 | D3 | semidirect |
| 14. C3×C32⋊C9 | C2×C3 | semidirect |
| 31. C3×3−1+2 | C3⋊D3 | semidirect |
| 38. C32×C9 | C3×D3 | semidirect |
| 49. C32⋊C9 | C3×D3 | semidirect |
| 50. C3⋊(C3⋊D3) | 3−1+2 | semidirect |
| 75. C33 | C2×3−1+2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624883 | 2 |
| C3×C3⋊((C3⋊D3)⋊C3) | 3 |
| C3⋊((C3⋊D3)⋊C9) | 3 |
| #92262 | 3 |
| #92259 | 3 |