Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
156 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 2. C2×C4×D35 | C2 | semidirect |
| 3. C5×C7×C22⋊C4 | C2 | semidirect |
| 4. C22⋊Dic35 | C2 | semidirect |
| 5. #10587902 | C2 | semidirect |
| 6. C4⋊Dic35 | C2 | semidirect |
| 7. #10587900 | C2 | semidirect |
| 33. C7×C22⋊C4 | D5 | semidirect |
| 40. C5×C22⋊C4 | D7 | semidirect |
| 68. C5×C7 | #123 | semidirect |
| 100. C22⋊C4 | D35 | semidirect |
| 120. C7 | #4029 | semidirect |
| 121. C5 | #6446 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊D35 | 2 |
| C2×C4×D35 | 2 |
| C5×C7×C22⋊C4 | 2 |
| C22⋊Dic35 | 2 |
| #10587902 | 2 |
| C4⋊Dic35 | 2 |
| #10587900 | 2 |
| #6446 | 5 |
| #4029 | 7 |