Finite Group DatabasebetaFinite Group DatabasebetaOrder 9477.
1304 conjugacy classes of subgroups; only the 476 normal subgroups are shown.
This group has 1304 conjugacy classes of subgroups — too many to draw. Only its 476 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 | C32 | C34×C13 |
| LCS | G ▷ C32 ▷ C3 ▷ 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×C13×3−1+2 | C3 | semidirect |
| 2. C32×C13×H(3,𝔽3) | C3 | semidirect |
| 3. C13×#6911 | C3 | direct (N × H) |
| 4. C3×C13×#732 | C3 | semidirect |
| 9. C3×C13×3−1+2 | C32 | semidirect |
| 12. C3×C13×H(3,𝔽3) | C32 | semidirect |
| 13. C3×C13×H(3,𝔽3) | C32 | semidirect |
| 14. C32×C9×C13 | C32 | semidirect |
| 15. C13×#732 | C32 | semidirect |
| 16. C3×#6911 | C13 | direct (N × H) |
| 28. C13×H(3,𝔽3) | C33 | semidirect |
| 31. C3×C9×C13 | C33 | semidirect |
| 32. C32×3−1+2 | C3×C13 | semidirect |
| 33. C32×H(3,𝔽3) | C3×C13 | semidirect |
| 34. #6911 | C3×C13 | direct (N × H) |
| 35. C3×#732 | C3×C13 | semidirect |
| 52. C3×3−1+2 | C32×C13 | semidirect |
| 55. C3×H(3,𝔽3) | C32×C13 | semidirect |
| 56. C3×H(3,𝔽3) | C32×C13 | semidirect |
| 57. C32×C9 | C32×C13 | semidirect |
| 58. #732 | C32×C13 | semidirect |
| 63. C3×C13 | #6911 | direct (N × H) |
| 76. H(3,𝔽3) | C33×C13 | semidirect |
| 79. C3×C9 | C33×C13 | semidirect |
| 80. C13 | C3×#6911 | direct (N × H) |
| 97. C3 | C13×#6911 | direct (N × H) |