Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
136 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 136 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 |
|---|---|---|
| 1. D7×D20 | C2 | semidirect |
| 2. #10587945 | C2 | semidirect |
| 3. #10587894 | C2 | semidirect |
| 4. C7×D40 | C2 | semidirect |
| 5. C5×#1131 | C2 | semidirect |
| 6. #10587848 | C2 | semidirect |
| 7. #10587843 | C2 | semidirect |
| 10. Dic70 | C22 | semidirect |
| 12. C7×D20 | C22 | semidirect |
| 17. C5×C7×C8 | C22 | semidirect |
| 18. C5×C7⋊C8 | C22 | semidirect |
| 35. #1131 | D5 | semidirect |
| 40. D40 | D7 | semidirect |
| 57. C7×C8 | C2×D5 | semidirect |
| 58. C7⋊C8 | C2×D5 | semidirect |
| 65. D20 | C2×D7 | semidirect |
| 69. C5×C8 | C2×D7 | semidirect |
| 70. C5×C7 | AGL(1,ℤ/8) | semidirect |
| 115. C8 | D5×D7 | semidirect |
| 116. C7 | #4054 | semidirect |
| 117. C5 | #6474 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D7×D20 | 2 |
| #10587945 | 2 |
| #10587894 | 2 |
| C7×D40 | 2 |
| C5×#1131 | 2 |
| #10587848 | 2 |
| #10587843 | 2 |
| #6474 | 5 |
| #4054 | 7 |