Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
758 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 152 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C33 | C33 |
| commutator, Frattini, cosocle | C33 | C2×C33 |
| prime radical | C2×C32×H(3,𝔽3) | C3 |
| LCS | G ▷ C33 ▷ C1 | |
| UCS | C1 ◁ C2×C33 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10624563 | C2 | direct (N × H) |
| 2. C2×C32×3−1+2 | C3 | semidirect |
| 4. C2×C3×C32⋊C9 | C3 | semidirect |
| 5. C2×C3×C32⋊C9 | C3 | semidirect |
| 6. C32×3−1+2 | C2×C3 | semidirect |
| 8. C3×C32⋊C9 | C2×C3 | semidirect |
| 9. C3×C32⋊C9 | C2×C3 | semidirect |
| 38. C2×C33 | 3−1+2 | semidirect |
| 46. C2×C3×C9 | H(3,𝔽3) | semidirect |
| 55. C33 | C2×3−1+2 | semidirect |
| 63. C3×C9 | C2×H(3,𝔽3) | semidirect |
| 106. C2 | #10624563 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624563 | 2 |
| C2×C32×3−1+2 | 3 |
| C2×C32×H(3,𝔽3) | 3 |
| C2×C3×C32⋊C9 | 3 |