Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
152 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 44 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. C5×D4×D7 | C2 | semidirect |
| 2. D7×D20 | C2 | semidirect |
| 3. #10587903 | C2 | semidirect |
| 4. C7×#686 | C2 | semidirect |
| 5. #10587842 | C2 | semidirect |
| 6. #10587841 | C2 | semidirect |
| 7. D7×#168 | C2 | semidirect |
| 10. C5×C7×D4 | C22 | semidirect |
| 11. D140 | C22 | semidirect |
| 12. C7×D20 | C22 | semidirect |
| 14. C5×D28 | C22 | semidirect |
| 17. C7⋊#168 | C22 | semidirect |
| 18. C7×#168 | C22 | semidirect |
| 31. D4×D7 | D5 | semidirect |
| 42. #686 | D7 | direct (N × H) |
| 48. C5×D7 | D8 | semidirect |
| 53. C7×D4 | C2×D5 | semidirect |
| 57. D28 | C2×D5 | semidirect |
| 65. C5×D4 | C2×D7 | semidirect |
| 69. D20 | C2×D7 | semidirect |
| 71. #168 | C2×D7 | semidirect |
| 72. C5×C7 | C2×D8 | semidirect |
| 104. D7 | #686 | direct (N × H) |
| 118. D4 | D5×D7 | semidirect |
| 122. C7 | C2×#686 | semidirect |
| 123. C5 | D7×D8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D4×D7 | 2 |
| D7×D20 | 2 |
| #10587903 | 2 |
| C7×#686 | 2 |
| #10587842 | 2 |
| #10587841 | 2 |
| D7×#168 | 2 |
| D7×D8 | 5 |
| C2×#686 | 7 |