Finite Group DatabasebetaFinite Group DatabasebetaOrder 8019.
1082 conjugacy classes of subgroups; only the 482 normal subgroups are shown.
This group has 1082 conjugacy classes of subgroups — too many to draw. Only its 482 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. C3×C11×#737 | C3 | semidirect |
| 2. C32×C11×3−1+2 | C3 | semidirect |
| 3. C11×#6893 | C3 | semidirect |
| 4. C11×C9⋊H(3,𝔽3) | C3 | semidirect |
| 5. C11×C9⋊H(3,𝔽3) | C3 | semidirect |
| 6. C11×#6891 | C3 | semidirect |
| 8. C9×C11×H(3,𝔽3) | C3 | semidirect |
| 9. C3×C11×C32⋊C9 | C3 | semidirect |
| 17. C3×C11×3−1+2 | C32 | semidirect |
| 23. C32×C9×C11 | C32 | semidirect |
| 29. C11×C32⋊C9 | C32 | semidirect |
| 30. C11×C32⋊C9 | C32 | semidirect |
| 31. #10624896 | C11 | direct (N × H) |
| 43. C11×3−1+2 | H(3,𝔽3) | semidirect |
| 55. C3×#737 | C3×C11 | semidirect |
| 56. C32×3−1+2 | C3×C11 | semidirect |
| 57. #6893 | C3×C11 | semidirect |
| 58. C9⋊H(3,𝔽3) | C3×C11 | semidirect |
| 59. C9⋊H(3,𝔽3) | C3×C11 | semidirect |
| 60. #6891 | C3×C11 | semidirect |
| 62. C9×H(3,𝔽3) | C3×C11 | semidirect |
| 63. C3×C32⋊C9 | C3×C11 | semidirect |
| 77. C32×C11 | #737 | semidirect |
| 91. C3×3−1+2 | C32×C11 | semidirect |
| 97. C32×C9 | C32×C11 | semidirect |
| 103. C32⋊C9 | C32×C11 | semidirect |
| 104. C32⋊C9 | C32×C11 | semidirect |
| 123. 3−1+2 | C11×H(3,𝔽3) | semidirect |
| 135. C11 | #10624896 | direct (N × H) |
| 149. C32 | C11×#737 | semidirect |