Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
136 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 44 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×D140 | C2 | semidirect |
| 2. C7×#709 | C2 | semidirect |
| 3. C5×#1136 | C2 | semidirect |
| 4. #10587849 | C2 | semidirect |
| 5. #10587843 | C2 | semidirect |
| 11. C7×D20 | C22 | semidirect |
| 13. C7×Dic10 | C22 | semidirect |
| 14. C5×C7⋊C8 | C22 | semidirect |
| 28. #1136 | D5 | semidirect |
| 29. #709 | D7 | semidirect |
| 46. C7⋊C8 | C2×D5 | semidirect |
| 52. D20 | C2×D7 | semidirect |
| 54. Dic10 | C2×D7 | semidirect |
| 56. C5×C7 | AGL(1,ℤ/8) | semidirect |
| 94. C7 | #4054 | semidirect |
| 95. C5 | #6512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D140 | 2 |
| C7×#709 | 2 |
| C5×#1136 | 2 |
| #10587849 | 2 |
| #10587843 | 2 |
| #6512 | 5 |
| #4054 | 7 |