Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
152 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 52 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×C7×D20 | C2 | semidirect |
| 2. C2×C5×D28 | C2 | semidirect |
| 3. C2×C7⋊#168 | C2 | semidirect |
| 4. #10587841 | C2 | direct (N × H) |
| 9. C7×D20 | C22 | semidirect |
| 11. C5×D28 | C22 | semidirect |
| 12. C7⋊#168 | C22 | semidirect |
| 23. C2×D28 | D5 | semidirect |
| 27. C2×D20 | D7 | semidirect |
| 30. C2×C5×C7 | D8 | semidirect |
| 40. D28 | C2×D5 | semidirect |
| 48. D20 | C2×D7 | semidirect |
| 50. C5×C7 | C2×D8 | semidirect |
| 71. C2×C7 | #686 | semidirect |
| 75. C2×C5 | #1141 | semidirect |
| 86. C7 | C2×#686 | semidirect |
| 87. C5 | C2×#1141 | semidirect |
| 97. C2 | #10587841 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×D20 | 2 |
| C2×C5×D28 | 2 |
| C2×C7⋊#168 | 2 |
| #10587841 | 2 |
| C2×#1141 | 5 |
| C2×#686 | 7 |