Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
188 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 188 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. C2×C4×D5×C11 | C2 | semidirect |
| 2. C2×C4×C5×D11 | C2 | semidirect |
| 4. C4×Dic55 | C2 | semidirect |
| 5. #11724888 | C2 | semidirect |
| 6. #11724885 | C2 | semidirect |
| 7. (C2×D11)⋊Dic5 | C2 | semidirect |
| 17. #89167 | C4 | direct (N × H) |
| 22. C2×D5×C11 | C2×C4 | semidirect |
| 25. C2×C5×D11 | C2×C4 | semidirect |
| 26. C4×C5×C11 | D4 | semidirect |
| 28. Dic55 | C2×C4 | semidirect |
| 33. C2×C4×D11 | D5 | semidirect |
| 56. C2×C4×D5 | D11 | semidirect |
| 61. C5×C11 | C4×D4 | semidirect |
| 68. C2×D11 | C4×D5 | semidirect |
| 70. C4×C11 | C22⋊D5 | semidirect |
| 96. C2×D5 | C4×D11 | semidirect |
| 98. C4×C5 | C22⋊D11 | semidirect |
| 109. C11 | C4×C22⋊D5 | semidirect |
| 125. C5 | C4×C22⋊D11 | semidirect |
| 137. C4 | #89167 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D5×C11 | 2 |
| C2×C4×C5×D11 | 2 |
| C2×#89167 | 2 |
| C4×Dic55 | 2 |
| #11724888 | 2 |
| #11724885 | 2 |
| (C2×D11)⋊Dic5 | 2 |
| C4×C22⋊D11 | 5 |
| C4×C22⋊D5 | 11 |