Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
136 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 48 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. #10587931 | C2 | semidirect |
| 3. C7×#700 | C2 | semidirect |
| 4. #10587921 | C2 | semidirect |
| 5. #10587920 | C2 | semidirect |
| 13. C7⋊#170 | C22 | semidirect |
| 14. C7×#170 | C22 | semidirect |
| 33. #700 | D7 | semidirect |
| 36. D35 | M16 | semidirect |
| 56. #170 | C2×D7 | semidirect |
| 57. C5×C7 | C2×M16 | semidirect |
| 97. C7 | D5⋊M16 | semidirect |
| 98. C5 | D7×M16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D5×D7 | 2 |
| #10587931 | 2 |
| C7×#700 | 2 |
| #10587921 | 2 |
| #10587920 | 2 |
| D7×M16 | 5 |
| D5⋊M16 | 7 |