Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
156 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 66 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. C22×C4×C5×C11 | C2 | semidirect |
| 3. C11×C22⋊Dic5 | C2 | semidirect |
| 4. C11×#685 | C2 | semidirect |
| 5. C11×#683 | C2 | semidirect |
| 23. C22×C4×C11 | D5 | semidirect |
| 27. #4075 | C11 | direct (N × H) |
| 39. C22×C4×C5 | C2×C11 | semidirect |
| 41. C22⋊Dic5 | C2×C11 | semidirect |
| 42. #685 | C2×C11 | semidirect |
| 43. #683 | C2×C11 | semidirect |
| 44. C5×C11 | #123 | semidirect |
| 74. C22×C4 | D5×C11 | semidirect |
| 78. C11 | #4075 | direct (N × H) |
| 90. C5 | C11×#123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×C11 | 2 |
| C2×C11×C22⋊D5 | 2 |
| C11×C22⋊Dic5 | 2 |
| C11×#685 | 2 |
| C11×#683 | 2 |
| C11×#123 | 5 |
| #4075 | 11 |