Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
156 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 53 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×C4×AGL(1,𝔽11) | C2 | semidirect |
| 3. C22⋊C4×C11⋊C5 | C2 | semidirect |
| 4. C22⋊(Dic11⋊C5) | C2 | semidirect |
| 5. ((C2×D11)⋊C4)⋊C5 | C2 | semidirect |
| 6. C4⋊(Dic11⋊C5) | C2 | semidirect |
| 7. (Dic11⋊C4)⋊C5 | C2 | semidirect |
| 17. #66936 | C5 | semidirect |
| 31. C2×C4×D11 | C2×C5 | semidirect |
| 32. C11×C22⋊C4 | C2×C5 | semidirect |
| 33. C22⋊Dic11 | C2×C5 | semidirect |
| 34. (C2×D11)⋊C4 | C2×C5 | semidirect |
| 35. C4⋊Dic11 | C2×C5 | semidirect |
| 36. Dic11⋊C4 | C2×C5 | semidirect |
| 59. C11⋊C5 | #123 | semidirect |
| 105. C22⋊C4 | AGL(1,𝔽11) | semidirect |
| 106. C11 | C5×#123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊AGL(1,𝔽11) | 2 |
| C2×C4×AGL(1,𝔽11) | 2 |
| C22⋊C4×C11⋊C5 | 2 |
| C22⋊(Dic11⋊C5) | 2 |
| ((C2×D11)⋊C4)⋊C5 | 2 |
| C4⋊(Dic11⋊C5) | 2 |
| (Dic11⋊C4)⋊C5 | 2 |
| #66936 | 5 |
| C5×#123 | 11 |