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 |
|---|---|---|
| 3. #10587906 | C2 | semidirect |
| 4. C7×#689 | C2 | semidirect |
| 5. #10587851 | C2 | semidirect |
| 6. #10587850 | C2 | semidirect |
| 40. #689 | D7 | direct (N × H) |
| 43. C5×D7 | Q16 | semidirect |
| 66. C5×C7 | C2×Q16 | semidirect |
| 90. D7 | #689 | direct (N × H) |
| 104. C7 | C2×#689 | semidirect |
| 105. C5 | D7×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Q8×D7 | 2 |
| D7×Dic10 | 2 |
| #10587906 | 2 |
| C7×#689 | 2 |
| #10587851 | 2 |
| #10587850 | 2 |
| D7×#168 | 2 |
| D7×Q16 | 5 |
| C2×#689 | 7 |