Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
156 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 52 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×Dic35 | C2 | semidirect |
| 3. C5×C22⋊Dic7 | C2 | semidirect |
| 4. Dic7⋊Dic5 | C2 | semidirect |
| 5. #10587855 | C2 | semidirect |
| 26. C22⋊Dic7 | D5 | semidirect |
| 51. C5×C7 | #123 | semidirect |
| 89. C7 | #4032 | semidirect |
| 90. C5 | #6498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic35 | 2 |
| C2×C7×C22⋊D5 | 2 |
| C5×C22⋊Dic7 | 2 |
| Dic7⋊Dic5 | 2 |
| #10587855 | 2 |
| #6498 | 5 |
| #4032 | 7 |