Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
124 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 124 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. C5×C7×#41 | C2 | semidirect |
| 2. C7×#709 | C2 | semidirect |
| 3. C7×#689 | C2 | semidirect |
| 4. C7×#688 | C2 | semidirect |
| 5. C7×#687 | C2 | semidirect |
| 6. C7×#686 | C2 | semidirect |
| 7. C2×C7×#168 | C2 | semidirect |
| 20. #4096 | C7 | direct (N × H) |
| 29. C7×#41 | D5 | semidirect |
| 35. C5×#41 | C2×C7 | semidirect |
| 36. #709 | C2×C7 | semidirect |
| 37. #689 | C2×C7 | semidirect |
| 38. #688 | C2×C7 | semidirect |
| 39. #687 | C2×C7 | semidirect |
| 40. #686 | C2×C7 | semidirect |
| 41. C2×#168 | C2×C7 | semidirect |
| 68. C5×C7 | #135 | semidirect |
| 85. #41 | C7×D5 | semidirect |
| 110. C7 | #4096 | direct (N × H) |
| 111. C5 | C7×#135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C7×#41 | 2 |
| C7×#709 | 2 |
| C7×#689 | 2 |
| C7×#688 | 2 |
| C7×#687 | 2 |
| C7×#686 | 2 |
| C2×C7×#168 | 2 |
| C7×#135 | 5 |
| #4096 | 7 |