Finite Group DatabasebetaFinite Group Databasebeta← C32×C13×AΣL(1,𝔽27) #23745070
Order 9477.
2672 conjugacy classes of subgroups; only the 512 normal subgroups are shown.
This group has 2672 conjugacy classes of subgroups — too many to draw. Only its 512 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C33×C13 | H(3,𝔽3) |
| commutator, Frattini, cosocle | C32 | C34×C13 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C33×C13 ◁ C34×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C35×C13 | C3 | semidirect |
| 2. C32×C13×3−1+2 | C3 | semidirect |
| 3. C32×C13×H(3,𝔽3) | C3 | semidirect |
| 4. C3×C13×AΣL(1,𝔽27) | C3 | direct (N × H) |
| 10. C34×C13 | C32 | semidirect |
| 12. C3×C13×3−1+2 | C32 | semidirect |
| 14. C3×C13×H(3,𝔽3) | C32 | semidirect |
| 16. C13×AΣL(1,𝔽27) | C32 | direct (N × H) |
| 17. C32×AΣL(1,𝔽27) | C13 | direct (N × H) |
| 29. C33×C13 | C33 | semidirect |
| 31. C13×3−1+2 | C33 | semidirect |
| 33. C13×H(3,𝔽3) | C33 | semidirect |
| 35. C35 | C3×C13 | semidirect |
| 36. C32×3−1+2 | C3×C13 | semidirect |
| 37. C32×H(3,𝔽3) | C3×C13 | semidirect |
| 38. C3×AΣL(1,𝔽27) | C3×C13 | direct (N × H) |
| 47. C32×C13 | AΣL(1,𝔽27) | direct (N × H) |
| 57. C34 | C32×C13 | semidirect |
| 59. C3×3−1+2 | C32×C13 | semidirect |
| 61. C3×H(3,𝔽3) | C32×C13 | semidirect |
| 63. AΣL(1,𝔽27) | C32×C13 | direct (N × H) |
| 68. C3×C13 | C3×AΣL(1,𝔽27) | direct (N × H) |
| 81. C33 | C33×C13 | semidirect |
| 83. 3−1+2 | C33×C13 | semidirect |
| 85. H(3,𝔽3) | C33×C13 | semidirect |
| 87. C13 | C32×AΣL(1,𝔽27) | direct (N × H) |
| 96. C32 | C13×AΣL(1,𝔽27) | direct (N × H) |
| 105. C3 | C3×C13×AΣL(1,𝔽27) | direct (N × H) |