Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
148 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 1. C2×Q8×C11⋊C5 | C2 | semidirect |
| 4. C4⋊(Dic11⋊C5) | C2 | semidirect |
| 5. (Dic11⋊C4)⋊C5 | C2 | semidirect |
| 13. #66999 | C5 | semidirect |
| 17. C2×AGL(1,𝔽11) | Q8 | semidirect |
| 22. C2×Q8×C11 | C2×C5 | semidirect |
| 25. C4⋊Dic11 | C2×C5 | semidirect |
| 26. Dic11⋊C4 | C2×C5 | semidirect |
| 44. C11⋊C5 | C22⋊Q8 | semidirect |
| 48. C2×D11 | C5×Q8 | semidirect |
| 73. C2×Q8 | AGL(1,𝔽11) | semidirect |
| 78. C11 | C5×C22⋊Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×C11⋊C5 | 2 |
| C2×C4×AGL(1,𝔽11) | 2 |
| ((C2×D11)⋊C4)⋊C5 | 2 |
| C4⋊(Dic11⋊C5) | 2 |
| (Dic11⋊C4)⋊C5 | 2 |
| #66999 | 5 |
| C5×C22⋊Q8 | 11 |