Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
156 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 156 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. C22×C4×C5×C7 | C2 | semidirect |
| 3. C22⋊Dic35 | C2 | semidirect |
| 4. #10587902 | C2 | semidirect |
| 5. #10587900 | C2 | semidirect |
| 23. C22×C4×C7 | D5 | semidirect |
| 28. C22×C4×C5 | D7 | semidirect |
| 51. C5×C7 | #123 | semidirect |
| 70. C22×C4 | D35 | semidirect |
| 89. C7 | #4075 | semidirect |
| 90. C5 | #6492 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×C7 | 2 |
| C2×C22⋊D35 | 2 |
| C22⋊Dic35 | 2 |
| #10587902 | 2 |
| #10587900 | 2 |
| #6492 | 5 |
| #4075 | 7 |