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 |
|---|---|---|
| 3. C7×#689 | C2 | semidirect |
| 4. C5×#1144 | C2 | semidirect |
| 5. #10587852 | C2 | semidirect |
| 6. #10587851 | C2 | semidirect |
| 32. #1144 | D5 | semidirect |
| 39. #689 | D7 | semidirect |
| 43. D35 | Q16 | semidirect |
| 66. C5×C7 | C2×Q16 | semidirect |
| 104. C7 | D5×Q16 | 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 |
|---|---|
| Q8×D35 | 2 |
| D35⋊Q8 | 2 |
| C7×#689 | 2 |
| C5×#1144 | 2 |
| #10587852 | 2 |
| #10587851 | 2 |
| #10587837 | 2 |
| D7×Q16 | 5 |
| D5×Q16 | 7 |