Finite Group DatabasebetaFinite Group DatabasebetaOrder 21780.
150 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C112 | C22×C5 |
| Frattini | C3 | D3×(C11⋊C5)⋊D11 |
| socle | C3×C112 | C2×C5×D3 |
| LCS | G ▷ C9×C112 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C9⋊((C11⋊C5)⋊D11) | C2 | semidirect |
| 2. C11×D9×C11⋊C5 | C2 | semidirect |
| 3. C9×(C11⋊C5)⋊D11 | C2 | semidirect |
| 5. C9×C11×C11⋊C5 | C22 | semidirect |
| 6. D9×C11⋊D11 | C5 | semidirect |
| 11. C9⋊(C11⋊D11) | C2×C5 | semidirect |
| 12. C112×D9 | C2×C5 | semidirect |
| 13. C9×C11⋊D11 | C2×C5 | semidirect |
| 20. (C11⋊C5)⋊D11 | D9 | direct (N × H) |
| 21. C9×C112 | C22×C5 | semidirect |
| 26. D9×C11⋊C5 | D11 | semidirect |
| 33. C11×C11⋊C5 | C2×D9 | semidirect |
| 35. C9×C11⋊C5 | C2×D11 | semidirect |
| 49. C11⋊D11 | C5×D9 | semidirect |
| 59. C11×D9 | AGL(1,𝔽11) | semidirect |
| 60. C11×D9 | C5×D11 | semidirect |
| 67. C112 | C2×C5×D9 | semidirect |
| 75. C9×C11 | C2×AGL(1,𝔽11) | semidirect |
| 76. C9×C11 | C2×C5×D11 | semidirect |
| 91. C11⋊C5 | D9×D11 | semidirect |
| 115. D9 | (C11⋊C5)⋊D11 | direct (N × H) |
| 119. C11 | D9×AGL(1,𝔽11) | semidirect |
| 120. C11 | C5×D9×D11 | semidirect |
| 124. C9 | C2×(C11⋊C5)⋊D11 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9⋊((C11⋊C5)⋊D11) | 2 |
| C11×D9×C11⋊C5 | 2 |
| C9×(C11⋊C5)⋊D11 | 2 |
| D3×(C11⋊C5)⋊D11 | 3 |
| D9×C11⋊D11 | 5 |
| C5×D9×D11 | 11 |
| D9×AGL(1,𝔽11) | 11 |