Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
328 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 127 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×C22⋊D55 | C2 | semidirect |
| 3. #11725031 | C2 | direct (N × H) |
| 4. C2×D220 | C2 | semidirect |
| 5. C2×C4×D55 | C2 | semidirect |
| 6. C2×Dic110 | C2 | semidirect |
| 11. C2×C4×C5×C11 | C22 | semidirect |
| 12. C22⋊D55 | C22 | semidirect |
| 14. D220 | C22 | semidirect |
| 15. C4×D55 | C22 | semidirect |
| 16. Dic110 | C22 | semidirect |
| 26. C22×C4×C11 | D5 | semidirect |
| 34. C2×C5×C11 | #41 | semidirect |
| 41. C2×C4×C11 | C2×D5 | semidirect |
| 47. C22×C4×C5 | D11 | semidirect |
| 53. C5×C11 | C2×#41 | semidirect |
| 66. C2×C4×C5 | C2×D11 | semidirect |
| 74. C2×C11 | #709 | semidirect |
| 90. C22×C4 | D55 | semidirect |
| 91. C11 | C2×#709 | semidirect |
| 93. C2×C5 | #4339 | semidirect |
| 105. C2×C4 | C2×D55 | semidirect |
| 106. C5 | C2×#4339 | semidirect |
| 117. C2 | #11725031 | direct (N × H) |
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×C22⋊D55 | 2 |
| #11725031 | 2 |
| C2×D220 | 2 |
| C2×C4×D55 | 2 |
| C2×Dic110 | 2 |
| C2×#4339 | 5 |
| C2×#709 | 11 |