Finite Group DatabasebetaFinite Group DatabasebetaOrder 9477.
948 conjugacy classes of subgroups; only the 470 normal subgroups are shown.
This group has 948 conjugacy classes of subgroups — too many to draw. Only its 470 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C13 | C32×H(3,𝔽3) |
| commutator, Frattini, cosocle | C32 | C34×C13 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C13 ◁ C3×C13×3−1+2 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×3−1+4 | C3 | semidirect |
| 2. C3×C13×#737 | C3 | semidirect |
| 3. C13×#6913 | C3 | semidirect |
| 4. C13×#6912 | C3 | semidirect |
| 5. C13×#6911 | C3 | semidirect |
| 6. C13×#6909 | C3 | semidirect |
| 7. C13×#6908 | C3 | semidirect |
| 8. C3×C13×#731 | C3 | semidirect |
| 11. C13×#737 | C32 | semidirect |
| 16. C3×C13×3−1+2 | C32 | semidirect |
| 20. C32×C9×C13 | C32 | semidirect |
| 21. C13×#733 | C32 | semidirect |
| 23. C13×#731 | C32 | semidirect |
| 24. C13×#731 | C32 | semidirect |
| 25. C13×AΣL(1,𝔽27) | C32 | semidirect |
| 26. #10624935 | C13 | direct (N × H) |
| 48. 3−1+4 | C3×C13 | semidirect |
| 49. C3×#737 | C3×C13 | semidirect |
| 50. #6913 | C3×C13 | semidirect |
| 51. #6912 | C3×C13 | semidirect |
| 52. #6911 | C3×C13 | semidirect |
| 53. #6909 | C3×C13 | semidirect |
| 54. #6908 | C3×C13 | semidirect |
| 55. C3×#731 | C3×C13 | semidirect |
| 70. #737 | C32×C13 | semidirect |
| 75. C3×3−1+2 | C32×C13 | semidirect |
| 79. C32×C9 | C32×C13 | semidirect |
| 80. #733 | C32×C13 | semidirect |
| 82. #731 | C32×C13 | semidirect |
| 83. #731 | C32×C13 | semidirect |
| 84. AΣL(1,𝔽27) | C32×C13 | semidirect |
| 111. C13 | #10624935 | direct (N × H) |