Finite Group DatabasebetaFinite Group DatabasebetaOrder 9477.
292 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 292 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×H(3,𝔽3) | C32 |
| 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×C13×3−1+2 | C3 | semidirect |
| 4. C3×C92×C13 | C3 | semidirect |
| 5. C13×3−1+2⋊C9 | C3 | semidirect |
| 7. C13×#6867 | C3 | semidirect |
| 14. C13×#731 | C9 | direct (N × H) |
| 22. C9×#731 | C13 | direct (N × H) |
| 26. C13×3−1+2 | C3×C9 | semidirect |
| 38. C3×C9×C13 | C3×C9 | semidirect |
| 42. C9×3−1+2 | C3×C13 | semidirect |
| 44. C3×C92 | C3×C13 | semidirect |
| 45. 3−1+2⋊C9 | C3×C13 | semidirect |
| 47. #6867 | C3×C13 | semidirect |
| 62. C9×C13 | #731 | direct (N × H) |
| 69. #731 | C9×C13 | direct (N × H) |
| 86. 3−1+2 | C3×C9×C13 | semidirect |
| 98. C3×C9 | C3×C9×C13 | semidirect |
| 101. C13 | C9×#731 | direct (N × H) |
| 116. C9 | C13×#731 | direct (N × H) |