Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
156 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 48 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×C4×C7×D5 | C2 | semidirect |
| 3. #10587902 | C2 | semidirect |
| 4. C5×Dic7⋊C4 | C2 | semidirect |
| 5. #10587858 | C2 | semidirect |
| 6. #10587856 | C2 | semidirect |
| 7. #10587855 | C2 | semidirect |
| 37. Dic7⋊C4 | D5 | semidirect |
| 39. C2×C4×D5 | D7 | semidirect |
| 68. C5×C7 | #123 | semidirect |
| 120. C7 | #4040 | semidirect |
| 121. C5 | #6492 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C7×D5 | 2 |
| C2×#63307 | 2 |
| #10587902 | 2 |
| C5×Dic7⋊C4 | 2 |
| #10587858 | 2 |
| #10587856 | 2 |
| #10587855 | 2 |
| #6492 | 5 |
| #4040 | 7 |