Finite Group DatabasebetaFinite Group DatabasebetaOrder 9477.
446 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C13 | C32⋊H(3,𝔽3) |
| commutator, Frattini, cosocle | C33 | C33×C13 |
| LCS | G ▷ C33 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C13 ◁ C33×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×3−1+4 | C3 | semidirect |
| 2. C13×#6912 | C3 | semidirect |
| 3. C13×#6911 | C3 | semidirect |
| 4. C13×#6910 | C3 | semidirect |
| 5. C13×#6909 | C3 | semidirect |
| 6. C13×#6909 | C3 | semidirect |
| 7. C3×C13×AΣL(1,𝔽27) | C3 | semidirect |
| 8. C3×C13×AΣL(1,𝔽27) | C3 | semidirect |
| 9. C3×C13×AΣL(1,𝔽27) | C3 | semidirect |
| 30. #10624762 | C13 | direct (N × H) |
| 66. 3−1+4 | C3×C13 | semidirect |
| 67. #6912 | C3×C13 | semidirect |
| 68. #6911 | C3×C13 | semidirect |
| 69. #6910 | C3×C13 | semidirect |
| 70. #6909 | C3×C13 | semidirect |
| 71. #6909 | C3×C13 | semidirect |
| 72. C3×AΣL(1,𝔽27) | C3×C13 | semidirect |
| 73. C3×AΣL(1,𝔽27) | C3×C13 | semidirect |
| 74. C3×AΣL(1,𝔽27) | C3×C13 | semidirect |
| 157. C13 | #10624762 | direct (N × H) |