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×C7×Dic10 | C2 | semidirect |
| 4. C5×Dic7⋊C4 | C2 | semidirect |
| 5. #10587859 | C2 | semidirect |
| 6. #10587858 | C2 | semidirect |
| 22. C2×D35 | Q8 | semidirect |
| 35. Dic7⋊C4 | D5 | semidirect |
| 37. C2×Dic10 | D7 | semidirect |
| 65. C5×C7 | C22⋊Q8 | semidirect |
| 111. C7 | #4042 | semidirect |
| 112. C5 | #6509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×Dic10 | 2 |
| C2×#63304 | 2 |
| #10587902 | 2 |
| C5×Dic7⋊C4 | 2 |
| #10587859 | 2 |
| #10587858 | 2 |
| #10587856 | 2 |
| #6509 | 5 |
| #4042 | 7 |