Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
136 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 41 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. #10587989 | C2 | semidirect |
| 2. D4×D35 | C2 | semidirect |
| 3. C5×C7×D8 | C2 | semidirect |
| 4. #10587904 | C2 | semidirect |
| 5. #10587903 | C2 | semidirect |
| 6. #10587894 | C2 | semidirect |
| 7. #10587893 | C2 | semidirect |
| 10. C5×C7×D4 | C22 | semidirect |
| 16. Dic70 | C22 | semidirect |
| 17. C5×C7×C8 | C22 | semidirect |
| 18. C7⋊#168 | C22 | semidirect |
| 31. C7×D8 | D5 | semidirect |
| 38. C5×D8 | D7 | semidirect |
| 50. C7×D4 | C2×D5 | semidirect |
| 57. C7×C8 | C2×D5 | semidirect |
| 61. C5×D4 | C2×D7 | semidirect |
| 68. C5×C8 | C2×D7 | semidirect |
| 70. C5×C7 | AGL(1,ℤ/8) | semidirect |
| 93. D8 | D35 | semidirect |
| 111. D4 | C2×D35 | semidirect |
| 115. C8 | C2×D35 | semidirect |
| 116. C7 | #4057 | semidirect |
| 117. C5 | #6474 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10587989 | 2 |
| D4×D35 | 2 |
| C5×C7×D8 | 2 |
| #10587904 | 2 |
| #10587903 | 2 |
| #10587894 | 2 |
| #10587893 | 2 |
| #6474 | 5 |
| #4057 | 7 |