Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
992 conjugacy classes of subgroups; only the 476 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 476 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 | C3×H(3,𝔽3) |
| commutator, Frattini, cosocle | C32 | C2×C34 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C2×C32 ◁ C2×C32×C9 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#6913 | C2 | direct (N × H) |
| 2. C2×C3×#737 | C3 | semidirect |
| 3. C2×C32×3−1+2 | C3 | semidirect |
| 4. C2×#6913 | C3 | direct (N × H) |
| 5. C2×C3×#733 | C3 | semidirect |
| 6. C2×C3×#732 | C3 | semidirect |
| 7. C2×C3×#731 | C3 | semidirect |
| 8. C2×C3×AΣL(1,𝔽27) | C3 | semidirect |
| 9. C3×#737 | C2×C3 | semidirect |
| 10. C32×3−1+2 | C2×C3 | semidirect |
| 11. #6913 | C2×C3 | direct (N × H) |
| 12. C3×#733 | C2×C3 | semidirect |
| 13. C3×#732 | C2×C3 | semidirect |
| 14. C3×#731 | C2×C3 | semidirect |
| 15. C3×AΣL(1,𝔽27) | C2×C3 | semidirect |
| 18. C2×#737 | C32 | semidirect |
| 23. C2×C3×3−1+2 | C32 | semidirect |
| 29. C2×#733 | C32 | semidirect |
| 30. C2×#732 | C32 | semidirect |
| 31. C2×#731 | C32 | semidirect |
| 32. C2×AΣL(1,𝔽27) | C32 | semidirect |
| 35. #737 | C2×C32 | semidirect |
| 40. C3×3−1+2 | C2×C32 | semidirect |
| 46. #733 | C2×C32 | semidirect |
| 47. #732 | C2×C32 | semidirect |
| 48. #731 | C2×C32 | semidirect |
| 49. AΣL(1,𝔽27) | C2×C32 | semidirect |
| 128. C2×C3 | #6913 | direct (N × H) |
| 134. C3 | C2×#6913 | direct (N × H) |
| 136. C2 | C3×#6913 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6913 | 2 |
| C2×C3×#737 | 3 |
| C2×C32×3−1+2 | 3 |
| C2×#6913 | 3 |
| C2×C3×#733 | 3 |
| C2×C3×#732 | 3 |
| C2×C3×#731 | 3 |
| C2×C3×AΣL(1,𝔽27) | 3 |