Finite Group DatabasebetaFinite Group DatabasebetaOrder 9477.
1166 conjugacy classes of subgroups; only the 494 normal subgroups are shown.
This group has 1166 conjugacy classes of subgroups — too many to draw. Only its 494 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C3×C9×C13 | C33 |
| commutator, Frattini, cosocle | C32 | C34×C13 |
| socle | C32×C13 | C34 |
| prime radical | C13×C32⋊H(3,𝔽3) | C3 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C3×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. C33×C9×C13 | C3 | semidirect |
| 3. C13×#6893 | C3 | semidirect |
| 4. C13×C9⋊H(3,𝔽3) | C3 | semidirect |
| 5. C13×#6891 | C3 | semidirect |
| 7. C9×C13×H(3,𝔽3) | C3 | semidirect |
| 11. C3×C13×3−1+2 | C32 | semidirect |
| 19. C32×C9×C13 | C32 | semidirect |
| 21. C13×C32⋊C9 | C32 | semidirect |
| 22. #10624869 | C13 | direct (N × H) |
| 36. C3×C9×C13 | H(3,𝔽3) | semidirect |
| 41. C3×#737 | C3×C13 | semidirect |
| 42. C33×C9 | C3×C13 | semidirect |
| 43. #6893 | C3×C13 | semidirect |
| 44. C9⋊H(3,𝔽3) | C3×C13 | semidirect |
| 45. #6891 | C3×C13 | semidirect |
| 47. C9×H(3,𝔽3) | C3×C13 | semidirect |
| 55. C32×C13 | #737 | semidirect |
| 64. C3×3−1+2 | C32×C13 | semidirect |
| 72. C32×C9 | C32×C13 | semidirect |
| 74. C32⋊C9 | C32×C13 | semidirect |
| 93. C3×C9 | C13×H(3,𝔽3) | semidirect |
| 98. C13 | #10624869 | direct (N × H) |
| 106. C32 | C13×#737 | semidirect |