Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
764 conjugacy classes of subgroups; only the 440 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 440 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×C32 | C34 |
| commutator, Frattini, cosocle | C32 | C2×C34 |
| prime radical | C2×C32⋊H(3,𝔽3) | C3 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C2×C32 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10624888 | C2 | direct (N × H) |
| 2. C2×#6893 | C3 | semidirect |
| 3. C2×C9⋊H(3,𝔽3) | C3 | semidirect |
| 4. C2×C9⋊H(3,𝔽3) | C3 | semidirect |
| 5. C2×#6891 | C3 | semidirect |
| 7. C2×C9×H(3,𝔽3) | C3 | semidirect |
| 8. C2×C3×C32⋊C9 | C3 | semidirect |
| 9. #6893 | C2×C3 | semidirect |
| 10. C9⋊H(3,𝔽3) | C2×C3 | semidirect |
| 11. C9⋊H(3,𝔽3) | C2×C3 | semidirect |
| 12. #6891 | C2×C3 | semidirect |
| 14. C9×H(3,𝔽3) | C2×C3 | semidirect |
| 15. C3×C32⋊C9 | C2×C3 | semidirect |
| 18. C2×C3×3−1+2 | C32 | semidirect |
| 24. C2×C32×C9 | C32 | semidirect |
| 30. C2×C32⋊C9 | C32 | semidirect |
| 31. C2×C32⋊C9 | C32 | semidirect |
| 34. C3×3−1+2 | C2×C32 | semidirect |
| 40. C32×C9 | C2×C32 | semidirect |
| 46. C32⋊C9 | C2×C32 | semidirect |
| 47. C32⋊C9 | C2×C32 | semidirect |
| 134. C2 | #10624888 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624888 | 2 |
| C2×#6893 | 3 |
| C2×C9⋊H(3,𝔽3) | 3 |
| C2×#6891 | 3 |
| C2×C32⋊H(3,𝔽3) | 3 |
| C2×C9×H(3,𝔽3) | 3 |
| C2×C3×C32⋊C9 | 3 |