Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
124 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 46 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. #10587935 | C2 | semidirect |
| 3. C2×C7×#170 | C2 | semidirect |
| 4. #10587922 | C2 | semidirect |
| 5. #10587921 | C2 | semidirect |
| 6. #10587920 | C2 | semidirect |
| 7. D7×#170 | C2 | semidirect |
| 39. C2×#170 | D7 | semidirect |
| 68. C5×C7 | #131 | semidirect |
| 110. C7 | #4131 | semidirect |
| 111. C5 | #6464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10587952 | 2 |
| #10587935 | 2 |
| C2×C7×#170 | 2 |
| #10587922 | 2 |
| #10587921 | 2 |
| #10587920 | 2 |
| D7×#170 | 2 |
| #6464 | 5 |
| #4131 | 7 |