Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
264 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 114 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. C22×C4×C5×C11 | C2 | semidirect |
| 3. C22×C5×Dic11 | C2 | semidirect |
| 4. C5×(C2×D11)⋊C4 | C2 | direct (N × H) |
| 8. C22×C5×D11 | C4 | semidirect |
| 11. C2×C4×C5×C11 | C22 | semidirect |
| 13. C2×C5×Dic11 | C22 | semidirect |
| 14. C2×(C2×D11)⋊C4 | C5 | direct (N × H) |
| 22. C2×C5×D11 | C2×C4 | semidirect |
| 26. C22×C4×C11 | C2×C5 | semidirect |
| 27. C22×Dic11 | C2×C5 | semidirect |
| 28. (C2×D11)⋊C4 | C2×C5 | direct (N × H) |
| 30. C2×C5×C11 | C22⋊C4 | semidirect |
| 38. C22×D11 | C4×C5 | semidirect |
| 41. C2×C4×C11 | C22×C5 | semidirect |
| 43. C2×Dic11 | C22×C5 | semidirect |
| 46. C22×C4×C5 | D11 | semidirect |
| 48. C5×C11 | C2×C22⋊C4 | semidirect |
| 56. C2×D11 | C2×C4×C5 | semidirect |
| 67. C2×C4×C5 | C2×D11 | semidirect |
| 69. C2×C11 | C5×C22⋊C4 | semidirect |
| 86. C22×C4 | C5×D11 | semidirect |
| 88. C11 | C2×C5×C22⋊C4 | semidirect |
| 90. C2×C5 | (C2×D11)⋊C4 | direct (N × H) |
| 102. C2×C4 | C2×C5×D11 | semidirect |
| 103. C5 | C2×(C2×D11)⋊C4 | direct (N × H) |
| 115. C2 | C5×(C2×D11)⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C5×D11 | 2 |
| C22×C4×C5×C11 | 2 |
| C22×C5×Dic11 | 2 |
| C5×(C2×D11)⋊C4 | 2 |
| C2×(C2×D11)⋊C4 | 5 |
| C2×C5×C22⋊C4 | 11 |