Finite Group DatabasebetaFinite Group DatabasebetaOrder 9477.
1244 conjugacy classes of subgroups; only the 518 normal subgroups are shown.
This group has 1244 conjugacy classes of subgroups — too many to draw. Only its 518 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 | C34 |
| commutator, Frattini, cosocle | C32 | C34×C13 |
| prime radical | C32×C13×H(3,𝔽3) | C3 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×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. C13×C9⋊H(3,𝔽3) | C3 | semidirect |
| 4. C13×#6891 | C3 | semidirect |
| 5. C9×C13×H(3,𝔽3) | C3 | semidirect |
| 10. C3×C13×3−1+2 | C32 | semidirect |
| 14. C32×C9×C13 | C32 | semidirect |
| 15. C13×C32⋊C9 | C32 | semidirect |
| 16. C13×C32⋊C9 | C32 | semidirect |
| 17. H(3,𝔽3)×3−1+2 | C13 | direct (N × H) |
| 26. C13×3−1+2 | H(3,𝔽3) | direct (N × H) |
| 28. C13×H(3,𝔽3) | 3−1+2 | direct (N × H) |
| 32. C32×3−1+2 | C3×C13 | semidirect |
| 34. C9⋊H(3,𝔽3) | C3×C13 | semidirect |
| 35. #6891 | C3×C13 | semidirect |
| 36. C9×H(3,𝔽3) | C3×C13 | semidirect |
| 46. C32×C13 | C3×3−1+2 | semidirect |
| 49. C9×C13 | C3×H(3,𝔽3) | semidirect |
| 54. C3×3−1+2 | C32×C13 | semidirect |
| 58. C32×C9 | C32×C13 | semidirect |
| 59. C32⋊C9 | C32×C13 | semidirect |
| 60. C32⋊C9 | C32×C13 | semidirect |
| 75. 3−1+2 | C13×H(3,𝔽3) | direct (N × H) |
| 77. H(3,𝔽3) | C13×3−1+2 | direct (N × H) |
| 81. C13 | H(3,𝔽3)×3−1+2 | direct (N × H) |
| 91. C32 | C3×C13×3−1+2 | semidirect |
| 94. C9 | C3×C13×H(3,𝔽3) | semidirect |