Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
152 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 55 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×C5×D4×C11 | C2 | semidirect |
| 2. C2×D220 | C2 | semidirect |
| 3. #11724933 | C2 | direct (N × H) |
| 4. C2×C11⋊#168 | C2 | semidirect |
| 8. C5×D4×C11 | C22 | semidirect |
| 11. D220 | C22 | semidirect |
| 12. C11⋊#168 | C22 | semidirect |
| 21. C2×D4×C11 | D5 | semidirect |
| 27. C2×C5×C11 | D8 | semidirect |
| 33. D4×C11 | C2×D5 | semidirect |
| 38. C2×C5×D4 | D11 | semidirect |
| 42. C5×C11 | C2×D8 | semidirect |
| 53. C5×D4 | C2×D11 | semidirect |
| 60. C2×C11 | #686 | semidirect |
| 71. C2×D4 | D55 | semidirect |
| 74. C11 | C2×#686 | semidirect |
| 76. C2×C5 | #4323 | semidirect |
| 84. D4 | C2×D55 | semidirect |
| 87. C5 | C2×#4323 | semidirect |
| 97. C2 | #11724933 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D4×C11 | 2 |
| C2×D220 | 2 |
| #11724933 | 2 |
| C2×C11⋊#168 | 2 |
| C2×#4323 | 5 |
| C2×#686 | 11 |