Finite Group DatabasebetaFinite Group DatabasebetaOrder 9477.
560 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 560 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×H(5,𝔽3) | C3 | semidirect |
| 2. C13×#6911 | C3 | semidirect |
| 3. C13×#6909 | C3 | semidirect |
| 4. C3×C13×AΣL(1,𝔽27) | C3 | semidirect |
| 5. C13×C32⋊H(3,𝔽3) | C3 | semidirect |
| 6. C34×C13 | C32 | semidirect |
| 7. C3×C13×3−1+2 | C32 | semidirect |
| 13. C3×C13×H(3,𝔽3) | C32 | semidirect |
| 17. UT(4,𝔽3) | C13 | direct (N × H) |
| 24. C33×C13 | H(3,𝔽3) | semidirect |
| 35. C13×H(3,𝔽3) | H(3,𝔽3) | semidirect |
| 37. H(5,𝔽3) | C3×C13 | semidirect |
| 38. #6911 | C3×C13 | semidirect |
| 39. #6909 | C3×C13 | semidirect |
| 40. C3×AΣL(1,𝔽27) | C3×C13 | semidirect |
| 41. C32⋊H(3,𝔽3) | C3×C13 | semidirect |
| 57. C34 | C32×C13 | semidirect |
| 58. C3×3−1+2 | C32×C13 | semidirect |
| 64. C3×H(3,𝔽3) | C32×C13 | semidirect |
| 81. C33 | C13×H(3,𝔽3) | semidirect |
| 92. H(3,𝔽3) | C13×H(3,𝔽3) | semidirect |
| 94. C13 | UT(4,𝔽3) | direct (N × H) |