Finite Group DatabasebetaFinite Group DatabasebetaOrder 9477.
470 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
| 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. C3×C13×#737 | C3 | semidirect |
| 2. C3×C13×#733 | C3 | semidirect |
| 3. C3×C13×#732 | C3 | semidirect |
| 4. C3×C13×#731 | C3 | semidirect |
| 5. C3×C13×#731 | C3 | semidirect |
| 6. C3×C13×AΣL(1,𝔽27) | C3 | semidirect |
| 7. C3×C13×AΣL(1,𝔽27) | C3 | semidirect |
| 8. C13×#6893 | C3 | semidirect |
| 9. C3×C13×C32⋊C9 | C3 | semidirect |
| 33. #10624746 | C13 | direct (N × H) |
| 71. C3×#737 | C3×C13 | semidirect |
| 72. C3×#733 | C3×C13 | semidirect |
| 73. C3×#732 | C3×C13 | semidirect |
| 74. C3×#731 | C3×C13 | semidirect |
| 75. C3×#731 | C3×C13 | semidirect |
| 76. C3×AΣL(1,𝔽27) | C3×C13 | semidirect |
| 77. C3×AΣL(1,𝔽27) | C3×C13 | semidirect |
| 78. #6893 | C3×C13 | semidirect |
| 79. C3×C32⋊C9 | C3×C13 | semidirect |
| 171. C13 | #10624746 | direct (N × H) |