Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
136 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 44 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. #10587987 | C2 | semidirect |
| 2. C2×C5×D28 | C2 | semidirect |
| 3. C7×#681 | C2 | semidirect |
| 4. #10587846 | C2 | semidirect |
| 5. #10587842 | C2 | semidirect |
| 9. D140 | C22 | semidirect |
| 11. Dic70 | C22 | semidirect |
| 14. C7×#168 | C22 | semidirect |
| 25. C2×D28 | D5 | semidirect |
| 33. #681 | D7 | semidirect |
| 55. #168 | C2×D7 | semidirect |
| 56. C5×C7 | AGL(1,ℤ/8) | semidirect |
| 94. C7 | #4078 | semidirect |
| 95. C5 | #6471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10587987 | 2 |
| C2×C5×D28 | 2 |
| C7×#681 | 2 |
| #10587846 | 2 |
| #10587842 | 2 |
| #6471 | 5 |
| #4078 | 7 |