Finite Group DatabasebetaFinite Group DatabasebetaOrder 9477.
992 conjugacy classes of subgroups; only the 476 normal subgroups are shown.
This group has 992 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 ◁ C32×C9×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C13×#737 | C3 | semidirect |
| 2. C32×C13×3−1+2 | C3 | semidirect |
| 3. C13×#6913 | C3 | direct (N × H) |
| 4. C3×C13×#733 | C3 | semidirect |
| 5. C3×C13×#732 | C3 | semidirect |
| 6. C3×C13×#731 | C3 | semidirect |
| 7. C3×C13×AΣL(1,𝔽27) | C3 | semidirect |
| 10. C13×#737 | C32 | semidirect |
| 15. C3×C13×3−1+2 | C32 | semidirect |
| 21. C13×#733 | C32 | semidirect |
| 22. C13×#732 | C32 | semidirect |
| 23. C13×#731 | C32 | semidirect |
| 24. C13×AΣL(1,𝔽27) | C32 | semidirect |
| 25. C3×#6913 | C13 | direct (N × H) |
| 49. C3×#737 | C3×C13 | semidirect |
| 50. C32×3−1+2 | C3×C13 | semidirect |
| 51. #6913 | C3×C13 | direct (N × H) |
| 52. C3×#733 | C3×C13 | semidirect |
| 53. C3×#732 | C3×C13 | semidirect |
| 54. C3×#731 | C3×C13 | semidirect |
| 55. C3×AΣL(1,𝔽27) | C3×C13 | semidirect |
| 72. #737 | C32×C13 | semidirect |
| 77. C3×3−1+2 | C32×C13 | semidirect |
| 83. #733 | C32×C13 | semidirect |
| 84. #732 | C32×C13 | semidirect |
| 85. #731 | C32×C13 | semidirect |
| 86. AΣL(1,𝔽27) | C32×C13 | semidirect |
| 91. C3×C13 | #6913 | direct (N × H) |
| 116. C13 | C3×#6913 | direct (N × H) |
| 135. C3 | C13×#6913 | direct (N × H) |