Finite Group DatabasebetaFinite Group DatabasebetaOrder 2640.
136 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3⋊(Dic11⋊C5) | C2 | semidirect |
| 3. C2×Dic3×C11⋊C5 | C2 | semidirect |
| 8. C2×C3×AGL(1,𝔽11) | C4 | semidirect |
| 11. (C2×D11)⋊Dic3 | C5 | semidirect |
| 20. C2×Dic33 | C2×C5 | semidirect |
| 21. C2×C11×Dic3 | C2×C5 | semidirect |
| 26. C2×AGL(1,𝔽11) | Dic3 | semidirect |
| 30. C3×C11⋊C5 | C22⋊C4 | semidirect |
| 34. C2×C3×D11 | C4×C5 | semidirect |
| 58. C11⋊C5 | #217 | semidirect |
| 63. C2×D11 | C5×Dic3 | semidirect |
| 69. C3×C11 | C5×C22⋊C4 | semidirect |
| 76. C2×Dic3 | AGL(1,𝔽11) | semidirect |
| 95. C11 | C5×#217 | semidirect |
| 114. C3 | ((C2×D11)⋊C4)⋊C5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×AGL(1,𝔽11) | 2 |
| C2×C3⋊(Dic11⋊C5) | 2 |
| C2×Dic3×C11⋊C5 | 2 |
| ((C2×D11)⋊C4)⋊C5 | 3 |
| (C2×D11)⋊Dic3 | 5 |
| C5×#217 | 11 |