Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
136 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 64 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. #10587898 | C2 | semidirect |
| 3. C7×#681 | C2 | semidirect |
| 4. #10587838 | C2 | semidirect |
| 5. D7×#168 | C2 | semidirect |
| 13. C7⋊#168 | C22 | semidirect |
| 14. C7×#168 | C22 | semidirect |
| 33. #681 | D7 | direct (N × H) |
| 38. C5×D7 | M16 | semidirect |
| 56. #168 | C2×D7 | semidirect |
| 57. C5×C7 | C2×M16 | semidirect |
| 83. D7 | #681 | direct (N × H) |
| 97. C7 | C2×#681 | semidirect |
| 98. C5 | D7×M16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×D7 | 2 |
| #10587898 | 2 |
| C7×#681 | 2 |
| #10587838 | 2 |
| D7×#168 | 2 |
| D7×M16 | 5 |
| C2×#681 | 7 |