Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
156 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 66 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. C22×C4×C5×C7 | C2 | semidirect |
| 3. C7×C22⋊Dic5 | C2 | semidirect |
| 4. C7×#685 | C2 | semidirect |
| 5. C7×#683 | C2 | semidirect |
| 14. #4075 | C7 | direct (N × H) |
| 24. C22×C4×C7 | D5 | semidirect |
| 28. C22×C4×C5 | C2×C7 | semidirect |
| 30. C22⋊Dic5 | C2×C7 | semidirect |
| 31. #685 | C2×C7 | semidirect |
| 32. #683 | C2×C7 | semidirect |
| 51. C5×C7 | #123 | semidirect |
| 70. C22×C4 | C7×D5 | semidirect |
| 89. C7 | #4075 | direct (N × H) |
| 90. C5 | C7×#123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×C7 | 2 |
| C2×C7×C22⋊D5 | 2 |
| C7×C22⋊Dic5 | 2 |
| C7×#685 | 2 |
| C7×#683 | 2 |
| C7×#123 | 5 |
| #4075 | 7 |