Finite Group DatabasebetaFinite Group DatabasebetaOrder 9477.
304 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 122 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 | C32 | C32×C9×C13 |
| Frattini, cosocle | C33 | C33×C13 |
| prime radical | C3×C13×AΣL(1,𝔽27) | C3 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C13 ◁ C32×C9×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C9×C13×3−1+2 | C3 | semidirect |
| 3. C9×C13×H(3,𝔽3) | C3 | semidirect |
| 4. C3×C13×C32⋊C9 | C3 | semidirect |
| 5. C13×3−1+2⋊C9 | C3 | semidirect |
| 6. C13×H(3,𝔽3)⋊C9 | C3 | semidirect |
| 7. C13×#6866 | C3 | semidirect |
| 14. C13×AΣL(1,𝔽27) | C9 | semidirect |
| 23. AΣL(1,𝔽27)⋊C9 | C13 | direct (N × H) |
| 29. C33×C13 | C3×C9 | semidirect |
| 32. C13×3−1+2 | C3×C9 | semidirect |
| 45. C9×3−1+2 | C3×C13 | semidirect |
| 46. C9×H(3,𝔽3) | C3×C13 | semidirect |
| 47. C3×C32⋊C9 | C3×C13 | semidirect |
| 48. 3−1+2⋊C9 | C3×C13 | semidirect |
| 49. H(3,𝔽3)⋊C9 | C3×C13 | semidirect |
| 50. #6866 | C3×C13 | semidirect |
| 76. AΣL(1,𝔽27) | C9×C13 | semidirect |
| 97. C33 | C3×C9×C13 | semidirect |
| 100. 3−1+2 | C3×C9×C13 | semidirect |
| 112. C13 | AΣL(1,𝔽27)⋊C9 | direct (N × H) |