Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
152 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 68 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. C4⋊Dic35 | C2 | semidirect |
| 3. C7×C4⋊Dic5 | C2 | semidirect |
| 5. Dic5×Dic7 | C2 | semidirect |
| 11. C4×C5×D7 | C4 | semidirect |
| 30. C4⋊Dic5 | D7 | semidirect |
| 41. C4×D7 | Dic5 | semidirect |
| 48. C5×C7 | #117 | semidirect |
| 85. C7 | #4072 | semidirect |
| 86. C5 | #6455 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×D7 | 2 |
| C4⋊Dic35 | 2 |
| C7×C4⋊Dic5 | 2 |
| (C2×D7)⋊Dic5 | 2 |
| Dic5×Dic7 | 2 |
| #6455 | 5 |
| #4072 | 7 |