Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
120 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 38 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. Q8×D35 | C2 | semidirect |
| 3. C7×#689 | C2 | semidirect |
| 4. C5×#1143 | C2 | semidirect |
| 5. #10587852 | C2 | semidirect |
| 6. #10587846 | C2 | semidirect |
| 7. #10587840 | C2 | semidirect |
| 32. #1143 | D5 | semidirect |
| 38. #689 | D7 | semidirect |
| 67. C5×C7 | #137 | semidirect |
| 107. C7 | #4061 | semidirect |
| 108. C5 | #6481 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D35 | 2 |
| #10587939 | 2 |
| C7×#689 | 2 |
| C5×#1143 | 2 |
| #10587852 | 2 |
| #10587846 | 2 |
| #10587840 | 2 |
| #6481 | 5 |
| #4061 | 7 |