Finite Group DatabasebetaFinite Group DatabasebetaOrder 9477.
328 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 128 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 | H(3,𝔽3) |
| commutator | C32 | C32×C9×C13 |
| Frattini, cosocle | C33 | C33×C13 |
| socle | C32×C13 | C3×H(3,𝔽3) |
| prime radical | C3×C13×#732 | C3 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C9×C13 ◁ C32×C9×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C9×C13×H(3,𝔽3) | C3 | semidirect |
| 3. C3×C92×C13 | C3 | semidirect |
| 4. C13×H(3,𝔽3)⋊C9 | C3 | semidirect |
| 5. C13×#6868 | C3 | semidirect |
| 11. C13×#732 | C9 | direct (N × H) |
| 16. C9×#732 | C13 | direct (N × H) |
| 20. C13×H(3,𝔽3) | C3×C9 | semidirect |
| 28. C3×C9×C13 | C3×C9 | semidirect |
| 32. C9×H(3,𝔽3) | C3×C13 | semidirect |
| 33. C3×C92 | C3×C13 | semidirect |
| 34. H(3,𝔽3)⋊C9 | C3×C13 | semidirect |
| 35. #6868 | C3×C13 | semidirect |
| 48. C9×C13 | #732 | direct (N × H) |
| 54. #732 | C9×C13 | direct (N × H) |
| 68. H(3,𝔽3) | C3×C9×C13 | semidirect |
| 76. C3×C9 | C3×C9×C13 | semidirect |
| 79. C13 | C9×#732 | direct (N × H) |
| 92. C9 | C13×#732 | direct (N × H) |