Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 40 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×Q8×D7 | C2 | semidirect |
| 3. #10587906 | C2 | semidirect |
| 4. C7×#688 | C2 | semidirect |
| 5. #10587851 | C2 | semidirect |
| 6. #10587845 | C2 | semidirect |
| 7. #10587838 | C2 | semidirect |
| 28. Q8×D7 | D5 | semidirect |
| 40. #688 | D7 | semidirect |
| 67. C5×C7 | #137 | semidirect |
| 107. C7 | #4088 | semidirect |
| 108. C5 | #6478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Q8×D7 | 2 |
| #10587945 | 2 |
| #10587906 | 2 |
| C7×#688 | 2 |
| #10587851 | 2 |
| #10587845 | 2 |
| #10587838 | 2 |
| #6478 | 5 |
| #4088 | 7 |