Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
136 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 58 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×C5×C7×D4 | C2 | semidirect |
| 2. C7×#709 | C2 | semidirect |
| 3. C7×#687 | C2 | semidirect |
| 4. C7×#686 | C2 | semidirect |
| 5. C7×#681 | C2 | semidirect |
| 11. C7×D20 | C22 | semidirect |
| 13. C7×Dic10 | C22 | semidirect |
| 14. C7×#168 | C22 | semidirect |
| 16. #4078 | C7 | direct (N × H) |
| 25. C2×C7×D4 | D5 | semidirect |
| 29. C2×C5×D4 | C2×C7 | semidirect |
| 30. #709 | C2×C7 | semidirect |
| 31. #687 | C2×C7 | semidirect |
| 32. #686 | C2×C7 | semidirect |
| 33. #681 | C2×C7 | semidirect |
| 52. D20 | C22×C7 | semidirect |
| 54. Dic10 | C22×C7 | semidirect |
| 55. #168 | C22×C7 | semidirect |
| 56. C5×C7 | AGL(1,ℤ/8) | semidirect |
| 73. C2×D4 | C7×D5 | semidirect |
| 94. C7 | #4078 | direct (N × H) |
| 95. C5 | C7×AGL(1,ℤ/8) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C7×D4 | 2 |
| C7×#709 | 2 |
| C7×#687 | 2 |
| C7×#686 | 2 |
| C7×#681 | 2 |
| C7×AGL(1,ℤ/8) | 5 |
| #4078 | 7 |