Finite Group DatabasebetaFinite Group DatabasebetaOrder 9477.
434 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 434 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 | 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 | C34×C13 | 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. C13×#6887 | C3 | semidirect |
| 3. C13×#6868 | C3 | semidirect |
| 4. C13×#6867 | C3 | semidirect |
| 10. C32×C9×C13 | C9 | semidirect |
| 17. #10624688 | C13 | direct (N × H) |
| 37. #6887 | C3×C13 | semidirect |
| 38. #6868 | C3×C13 | semidirect |
| 39. #6867 | C3×C13 | semidirect |
| 58. C32×C9 | C9×C13 | semidirect |
| 88. C13 | #10624688 | direct (N × H) |