Finite Group DatabasebetaFinite Group DatabasebetaOrder 9477.
1328 conjugacy classes of subgroups; only the 548 normal subgroups are shown.
This group has 1328 conjugacy classes of subgroups — too many to draw. Only its 548 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 | C33 |
| commutator, Frattini, cosocle | C32 | C34×C13 |
| prime radical | C32×C13×H(3,𝔽3) | C3 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C33×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 |
| 3. C33×C9×C13 | C3 | semidirect |
| 4. C13×C9⋊H(3,𝔽3) | C3 | direct (N × H) |
| 5. C3×C13×C32⋊C9 | C3 | semidirect |
| 6. C3×C13×C32⋊C9 | C3 | semidirect |
| 10. C3×C13×3−1+2 | C32 | semidirect |
| 17. C32×C9×C13 | C32 | semidirect |
| 18. C13×C32⋊C9 | C32 | semidirect |
| 19. C13×C32⋊C9 | C32 | semidirect |
| 20. C3×C9⋊H(3,𝔽3) | C13 | direct (N × H) |
| 26. C33×C13 | 3−1+2 | semidirect |
| 35. C3×C9×C13 | H(3,𝔽3) | semidirect |
| 39. C32×3−1+2 | C3×C13 | semidirect |
| 41. C33×C9 | C3×C13 | semidirect |
| 42. C9⋊H(3,𝔽3) | C3×C13 | direct (N × H) |
| 43. C3×C32⋊C9 | C3×C13 | semidirect |
| 44. C3×C32⋊C9 | C3×C13 | semidirect |
| 54. C32×C13 | C3×3−1+2 | semidirect |
| 59. C9×C13 | C3×H(3,𝔽3) | semidirect |
| 63. C3×3−1+2 | C32×C13 | semidirect |
| 70. C32×C9 | C32×C13 | semidirect |
| 71. C32⋊C9 | C32×C13 | semidirect |
| 72. C32⋊C9 | C32×C13 | semidirect |
| 75. C3×C13 | C9⋊H(3,𝔽3) | direct (N × H) |
| 84. C33 | C13×3−1+2 | semidirect |
| 93. C3×C9 | C13×H(3,𝔽3) | semidirect |
| 97. C13 | C3×C9⋊H(3,𝔽3) | direct (N × H) |
| 107. C32 | C3×C13×3−1+2 | semidirect |
| 112. C9 | C3×C13×H(3,𝔽3) | semidirect |
| 115. C3 | C13×C9⋊H(3,𝔽3) | direct (N × H) |