Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
136 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 136 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. #10587950 | C2 | semidirect |
| 2. #10587939 | C2 | semidirect |
| 3. #10587893 | C2 | semidirect |
| 4. C7×#677 | C2 | semidirect |
| 5. C5×D56 | C2 | semidirect |
| 6. #10587844 | C2 | semidirect |
| 7. #10587841 | C2 | semidirect |
| 11. C7×Dic10 | C22 | semidirect |
| 13. C5×D28 | C22 | semidirect |
| 17. C5×C7×C8 | C22 | semidirect |
| 18. C7⋊#168 | C22 | semidirect |
| 34. D56 | D5 | semidirect |
| 41. #677 | D7 | semidirect |
| 54. D28 | C2×D5 | semidirect |
| 57. C7×C8 | C2×D5 | semidirect |
| 67. Dic10 | C2×D7 | semidirect |
| 68. C5×C8 | C2×D7 | semidirect |
| 70. C5×C7 | AGL(1,ℤ/8) | semidirect |
| 115. C8 | D5×D7 | semidirect |
| 116. C7 | #4057 | semidirect |
| 117. C5 | #6477 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10587950 | 2 |
| #10587939 | 2 |
| #10587893 | 2 |
| C7×#677 | 2 |
| C5×D56 | 2 |
| #10587844 | 2 |
| #10587841 | 2 |
| #6477 | 5 |
| #4057 | 7 |