Finite Group DatabasebetaFinite Group DatabasebetaOrder 9477.
456 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 92 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 | C33 | C33×C13 |
| LCS | G ▷ C33 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C13 ◁ C33×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×H(5,𝔽3) | C3 | semidirect |
| 2. C13×#6910 | C3 | semidirect |
| 3. C13×#6909 | C3 | semidirect |
| 4. C13×#6909 | C3 | semidirect |
| 5. C3×C13×#732 | C3 | semidirect |
| 6. C3×C13×#731 | C3 | semidirect |
| 7. C13×#6893 | C3 | semidirect |
| 8. C3×C13×3−1+2 | C32 | semidirect |
| 9. C3×C13×3−1+2 | C32 | semidirect |
| 16. C3×C13×H(3,𝔽3) | C32 | semidirect |
| 17. C32×C9×C13 | C32 | semidirect |
| 24. #10624748 | C13 | direct (N × H) |
| 51. H(5,𝔽3) | C3×C13 | semidirect |
| 52. #6910 | C3×C13 | semidirect |
| 53. #6909 | C3×C13 | semidirect |
| 54. #6909 | C3×C13 | semidirect |
| 55. C3×#732 | C3×C13 | semidirect |
| 56. C3×#731 | C3×C13 | semidirect |
| 57. #6893 | C3×C13 | semidirect |
| 74. C3×3−1+2 | C32×C13 | semidirect |
| 75. C3×3−1+2 | C32×C13 | semidirect |
| 82. C3×H(3,𝔽3) | C32×C13 | semidirect |
| 83. C32×C9 | C32×C13 | semidirect |
| 124. C13 | #10624748 | direct (N × H) |