Finite Group DatabasebetaFinite Group DatabasebetaOrder 9477.
216 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 80 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, Frattini, cosocle | C33 | C33×C13 |
| prime radical | C3×C13×H(3,𝔽3) | C32 |
| LCS | G ▷ C33 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C13 ◁ C32×C9×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×#6895 | C3 | semidirect |
| 3. C13×#6887 | C3 | semidirect |
| 4. C3×C13×C9⋊C9 | C3 | semidirect |
| 5. C13×3−1+2⋊C9 | C3 | semidirect |
| 6. C13×3−1+2⋊C9 | C3 | semidirect |
| 7. C13×3−1+2⋊C9 | C3 | semidirect |
| 8. C13×3−1+2⋊C9 | C3 | semidirect |
| 9. C13×3−1+2⋊C9 | C3 | semidirect |
| 10. C13×3−1+2⋊C9 | C3 | semidirect |
| 35. #10624827 | C13 | direct (N × H) |
| 58. #6895 | C3×C13 | semidirect |
| 60. #6887 | C3×C13 | semidirect |
| 61. C3×C9⋊C9 | C3×C13 | semidirect |
| 62. 3−1+2⋊C9 | C3×C13 | semidirect |
| 63. 3−1+2⋊C9 | C3×C13 | semidirect |
| 64. 3−1+2⋊C9 | C3×C13 | semidirect |
| 65. 3−1+2⋊C9 | C3×C13 | semidirect |
| 66. 3−1+2⋊C9 | C3×C13 | semidirect |
| 67. 3−1+2⋊C9 | C3×C13 | semidirect |
| 142. C13 | #10624827 | direct (N × H) |