Finite Group DatabasebetaFinite Group DatabasebetaOrder 9477.
506 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 86 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 ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C13 ◁ C34×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×C13×H(3,𝔽3) | C3 | semidirect |
| 2. C13×#6891 | C3 | semidirect |
| 3. C13×C32⋊H(3,𝔽3) | C3 | semidirect |
| 4. C3×C13×C32⋊C9 | C3 | semidirect |
| 5. C13×#6856 | C3 | semidirect |
| 16. C3×C13×H(3,𝔽3) | C32 | semidirect |
| 22. C13×C32⋊C9 | C32 | semidirect |
| 23. C13×C32⋊C9 | C32 | semidirect |
| 24. #10624596 | C13 | direct (N × H) |
| 50. C32×H(3,𝔽3) | C3×C13 | semidirect |
| 51. #6891 | C3×C13 | semidirect |
| 52. C32⋊H(3,𝔽3) | C3×C13 | semidirect |
| 53. C3×C32⋊C9 | C3×C13 | semidirect |
| 54. #6856 | C3×C13 | semidirect |
| 94. C3×H(3,𝔽3) | C32×C13 | semidirect |
| 100. C32⋊C9 | C32×C13 | semidirect |
| 101. C32⋊C9 | C32×C13 | semidirect |
| 137. C13 | #10624596 | direct (N × H) |