Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
148 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 50 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×Dic70 | C2 | semidirect |
| 3. C7×#683 | C2 | semidirect |
| 5. #10587858 | C2 | semidirect |
| 6. Dic7⋊Dic5 | C2 | semidirect |
| 22. C2×C5×D7 | Q8 | semidirect |
| 42. #683 | D7 | semidirect |
| 65. C5×C7 | C22⋊Q8 | semidirect |
| 70. C2×D7 | Dic10 | semidirect |
| 111. C7 | #4024 | semidirect |
| 112. C5 | #6459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic70 | 2 |
| C2×D7×Dic5 | 2 |
| C7×#683 | 2 |
| C5×(C2×D7)⋊C4 | 2 |
| #10587858 | 2 |
| Dic7⋊Dic5 | 2 |
| (C2×D7)⋊Dic5 | 2 |
| #6459 | 5 |
| #4024 | 7 |