Finite Group DatabasebetaFinite Group DatabasebetaOrder 9477.
1196 conjugacy classes of subgroups; only the 476 normal subgroups are shown.
This group has 1196 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 | C32×C13 | C3×H(3,𝔽3) |
| commutator, Frattini, cosocle | C32 | C34×C13 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C13 ◁ C34×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×C13×3−1+2 | C3 | semidirect |
| 2. C32×C13×H(3,𝔽3) | C3 | semidirect |
| 3. C32×C13×H(3,𝔽3) | C3 | semidirect |
| 4. C13×#6909 | C3 | direct (N × H) |
| 5. C3×C13×AΣL(1,𝔽27) | C3 | semidirect |
| 8. C34×C13 | C32 | semidirect |
| 12. C3×C13×3−1+2 | C32 | semidirect |
| 13. C3×C13×3−1+2 | C32 | semidirect |
| 20. C3×C13×H(3,𝔽3) | C32 | semidirect |
| 21. C3×C13×H(3,𝔽3) | C32 | semidirect |
| 23. C13×AΣL(1,𝔽27) | C32 | semidirect |
| 24. C3×#6909 | C13 | direct (N × H) |
| 37. C33×C13 | C33 | semidirect |
| 41. C13×3−1+2 | C33 | semidirect |
| 49. C32×3−1+2 | C3×C13 | semidirect |
| 50. C32×H(3,𝔽3) | C3×C13 | semidirect |
| 51. C32×H(3,𝔽3) | C3×C13 | semidirect |
| 52. #6909 | C3×C13 | direct (N × H) |
| 53. C3×AΣL(1,𝔽27) | C3×C13 | semidirect |
| 74. C34 | C32×C13 | semidirect |
| 78. C3×3−1+2 | C32×C13 | semidirect |
| 79. C3×3−1+2 | C32×C13 | semidirect |
| 86. C3×H(3,𝔽3) | C32×C13 | semidirect |
| 87. C3×H(3,𝔽3) | C32×C13 | semidirect |
| 89. AΣL(1,𝔽27) | C32×C13 | semidirect |
| 96. C3×C13 | #6909 | direct (N × H) |
| 110. C33 | C33×C13 | semidirect |
| 114. 3−1+2 | C33×C13 | semidirect |
| 122. C13 | C3×#6909 | direct (N × H) |
| 147. C3 | C13×#6909 | direct (N × H) |