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 |
|---|---|---|
| 2. D35⋊Q8 | C2 | semidirect |
| 3. C7×#687 | C2 | semidirect |
| 4. C5×#1142 | C2 | semidirect |
| 5. #10587849 | C2 | semidirect |
| 6. #10587847 | C2 | semidirect |
| 7. #10587837 | C2 | semidirect |
| 13. C7×Dic10 | C22 | semidirect |
| 14. C5×Dic14 | C22 | semidirect |
| 17. C5×C7⋊C8 | C22 | semidirect |
| 18. C7×#168 | C22 | semidirect |
| 33. #1142 | D5 | semidirect |
| 40. #687 | D7 | semidirect |
| 46. D35 | SD16 | semidirect |
| 55. Dic14 | C2×D5 | semidirect |
| 57. C7⋊C8 | C2×D5 | semidirect |
| 66. Dic10 | C2×D7 | semidirect |
| 68. #168 | C2×D7 | semidirect |
| 69. C5×C7 | C2×SD16 | semidirect |
| 113. C7 | D5×SD16 | semidirect |
| 114. C5 | D7×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D35 | 2 |
| D35⋊Q8 | 2 |
| C7×#687 | 2 |
| C5×#1142 | 2 |
| #10587849 | 2 |
| #10587847 | 2 |
| #10587837 | 2 |
| D7×SD16 | 5 |
| D5×SD16 | 7 |