Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 120 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 |
|---|---|---|
| 2. C2×C5×Dic14 | C2 | semidirect |
| 3. C7×#681 | C2 | semidirect |
| 4. #10587851 | C2 | semidirect |
| 5. #10587847 | C2 | semidirect |
| 24. C2×Dic14 | D5 | semidirect |
| 32. #681 | D7 | semidirect |
| 54. C5×C7 | #137 | semidirect |
| 88. C7 | #4088 | semidirect |
| 89. C5 | #6472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10587987 | 2 |
| C2×C5×Dic14 | 2 |
| C7×#681 | 2 |
| #10587851 | 2 |
| #10587847 | 2 |
| #6472 | 5 |
| #4088 | 7 |