Finite Group DatabasebetaFinite Group DatabasebetaOrder 3168.
168 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle | C11×#157 | C23 |
| Fitting, socle, hypocenter | C32×C11 | C2×SD16 |
| prime radical | D11×GO+(4,𝔽2) | C2 |
| LCS | G ▷ C11×#157 ▷ C11×C3⋊D3 ▷ C32×C11 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D11×PSU(3,𝔽2) | C2 | semidirect |
| 3. AGL(1,𝔽9)⋊D11 | C2 | semidirect |
| 4. PSU(3,𝔽2)⋊D11 | C2 | semidirect |
| 5. #13097490 | C2 | semidirect |
| 6. C11×AΓL(1,𝔽9) | C2 | semidirect |
| 7. D11×AGL(1,𝔽9) | C2 | semidirect |
| 10. C11⋊PSU(3,𝔽2) | C22 | semidirect |
| 11. C11×PSU(3,𝔽2) | C22 | semidirect |
| 17. C11⋊AGL(1,𝔽9) | C22 | semidirect |
| 18. C11×AGL(1,𝔽9) | C22 | semidirect |
| 31. C3⋊D33 | SD16 | semidirect |
| 35. C32×D11 | SD16 | semidirect |
| 49. AΓL(1,𝔽9) | D11 | direct (N × H) |
| 57. C32×C11 | C2×SD16 | semidirect |
| 74. PSU(3,𝔽2) | C2×D11 | semidirect |
| 79. AGL(1,𝔽9) | C2×D11 | semidirect |
| 112. D11 | AΓL(1,𝔽9) | direct (N × H) |
| 132. C11 | C2×AΓL(1,𝔽9) | semidirect |
| 133. C32 | SD16×D11 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D11×PSU(3,𝔽2) | 2 |
| D11×GO+(4,𝔽2) | 2 |
| AGL(1,𝔽9)⋊D11 | 2 |
| PSU(3,𝔽2)⋊D11 | 2 |
| #13097490 | 2 |
| C11×AΓL(1,𝔽9) | 2 |
| D11×AGL(1,𝔽9) | 2 |
| SD16×D11 | 9 |
| C2×AΓL(1,𝔽9) | 11 |