Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
188 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
| 2. C2×C5×C22⋊D11 | C2 | semidirect |
| 3. C2×C5×D44 | C2 | semidirect |
| 4. C5×(C2×D11)⋊C4 | C2 | semidirect |
| 5. C5×C4⋊Dic11 | C2 | semidirect |
| 14. #66983 | C5 | direct (N × H) |
| 17. C22×C5×C11 | D4 | semidirect |
| 23. C4×C5×C11 | D4 | semidirect |
| 25. C22×C4×C11 | C2×C5 | semidirect |
| 26. C2×C22⋊D11 | C2×C5 | semidirect |
| 27. C2×D44 | C2×C5 | semidirect |
| 28. (C2×D11)⋊C4 | C2×C5 | semidirect |
| 29. C4⋊Dic11 | C2×C5 | semidirect |
| 46. C22×C4×C5 | D11 | semidirect |
| 49. C5×C11 | #121 | semidirect |
| 52. C22×C11 | C5×D4 | semidirect |
| 58. C4×C11 | C5×D4 | semidirect |
| 79. C22×C5 | D44 | semidirect |
| 83. C4×C5 | C22⋊D11 | semidirect |
| 86. C22×C4 | C5×D11 | semidirect |
| 89. C11 | C5×#121 | semidirect |
| 103. C5 | #66983 | direct (N × H) |
| 109. C22 | C5×D44 | semidirect |
| 113. C4 | C5×C22⋊D11 | 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×C5×C22⋊D11 | 2 |
| C2×C5×D44 | 2 |
| C5×(C2×D11)⋊C4 | 2 |
| C5×C4⋊Dic11 | 2 |
| #66983 | 5 |
| C5×#121 | 11 |