Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
328 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 116 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×Dic110 | C2 | semidirect |
| 2. C2×C11×D20 | C2 | semidirect |
| 3. C2×C4×C5×D11 | C2 | semidirect |
| 4. C2×#89167 | C2 | semidirect |
| 5. C2×D5×Dic11 | C2 | semidirect |
| 6. #11724989 | C2 | direct (N × H) |
| 11. Dic110 | C22 | semidirect |
| 12. C11×D20 | C22 | semidirect |
| 14. C4×C5×D11 | C22 | semidirect |
| 15. #89167 | C22 | semidirect |
| 16. D5×Dic11 | C22 | semidirect |
| 30. C2×C4×D11 | D5 | semidirect |
| 33. C2×C5×C11 | #41 | semidirect |
| 45. C4×D11 | C2×D5 | semidirect |
| 50. C2×D20 | D11 | semidirect |
| 53. C5×C11 | C2×#41 | semidirect |
| 69. D20 | C2×D11 | semidirect |
| 74. C2×C11 | #709 | semidirect |
| 91. C11 | C2×#709 | semidirect |
| 93. C2×C5 | #4341 | semidirect |
| 106. C5 | C2×#4341 | semidirect |
| 117. C2 | #11724989 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic110 | 2 |
| C2×C11×D20 | 2 |
| C2×C4×C5×D11 | 2 |
| C2×#89167 | 2 |
| C2×D5×Dic11 | 2 |
| #11724989 | 2 |
| C2×#4341 | 5 |
| C2×#709 | 11 |