Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
152 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 66 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. C2×C5×C7×D4 | C2 | semidirect |
| 2. C2×C7×D20 | C2 | semidirect |
| 3. C7×#686 | C2 | direct (N × H) |
| 4. C2×C7×#168 | C2 | semidirect |
| 8. C5×C7×D4 | C22 | semidirect |
| 11. C7×D20 | C22 | semidirect |
| 12. C7×#168 | C22 | semidirect |
| 14. C2×#686 | C7 | direct (N × H) |
| 23. C2×C7×D4 | D5 | semidirect |
| 26. C2×C5×D4 | C2×C7 | semidirect |
| 27. C2×D20 | C2×C7 | semidirect |
| 28. #686 | C2×C7 | direct (N × H) |
| 29. C2×#168 | C2×C7 | semidirect |
| 31. C2×C5×C7 | D8 | semidirect |
| 39. C7×D4 | C2×D5 | semidirect |
| 45. C5×D4 | C22×C7 | semidirect |
| 48. D20 | C22×C7 | semidirect |
| 49. #168 | C22×C7 | semidirect |
| 50. C5×C7 | C2×D8 | semidirect |
| 67. C2×D4 | C7×D5 | semidirect |
| 72. C2×C7 | #686 | direct (N × H) |
| 75. C2×C5 | C7×D8 | semidirect |
| 83. D4 | C2×C7×D5 | semidirect |
| 86. C7 | C2×#686 | direct (N × H) |
| 87. C5 | C2×C7×D8 | semidirect |
| 97. C2 | C7×#686 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C7×D4 | 2 |
| C2×C7×D20 | 2 |
| C7×#686 | 2 |
| C2×C7×#168 | 2 |
| C2×C7×D8 | 5 |
| C2×#686 | 7 |