Finite Group DatabasebetaFinite Group DatabasebetaOrder 9477.
404 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 152 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C13 | C3×H(3,𝔽3) |
| commutator | C32 | C32×C9×C13 |
| Frattini, cosocle | C33 | C33×C13 |
| prime radical | C34×C13 | C32 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C13 ◁ C34×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C13×3−1+2⋊C9 | C3 | semidirect |
| 10. C3×C13×3−1+2 | C9 | semidirect |
| 25. #10624699 | C13 | direct (N × H) |
| 38. C13×3−1+2 | C3×C9 | semidirect |
| 51. 3−1+2⋊C9 | C3×C13 | semidirect |
| 80. C3×3−1+2 | C9×C13 | semidirect |
| 116. 3−1+2 | C3×C9×C13 | semidirect |
| 125. C13 | #10624699 | direct (N × H) |