Finite Group DatabasebetaFinite Group DatabasebetaOrder 8019.
764 conjugacy classes of subgroups; only the 440 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 440 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×C11 | C34 |
| commutator, Frattini | C32 | C34×C11 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C11×#6893 | C3 | semidirect |
| 2. C11×C9⋊H(3,𝔽3) | C3 | semidirect |
| 3. C11×C9⋊H(3,𝔽3) | C3 | semidirect |
| 4. C11×#6891 | C3 | semidirect |
| 6. C9×C11×H(3,𝔽3) | C3 | semidirect |
| 7. C3×C11×C32⋊C9 | C3 | semidirect |
| 10. C3×C11×3−1+2 | C32 | semidirect |
| 16. C32×C9×C11 | C32 | semidirect |
| 22. C11×C32⋊C9 | C32 | semidirect |
| 23. C11×C32⋊C9 | C32 | semidirect |
| 24. #10624888 | C11 | direct (N × H) |
| 43. #6893 | C3×C11 | semidirect |
| 44. C9⋊H(3,𝔽3) | C3×C11 | semidirect |
| 45. C9⋊H(3,𝔽3) | C3×C11 | semidirect |
| 46. #6891 | C3×C11 | semidirect |
| 48. C9×H(3,𝔽3) | C3×C11 | semidirect |
| 49. C3×C32⋊C9 | C3×C11 | semidirect |
| 70. C3×3−1+2 | C32×C11 | semidirect |
| 76. C32×C9 | C32×C11 | semidirect |
| 82. C32⋊C9 | C32×C11 | semidirect |
| 83. C32⋊C9 | C32×C11 | semidirect |
| 109. C11 | #10624888 | direct (N × H) |