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. C8×D35 | C2 | semidirect |
| 4. C7×#677 | C2 | semidirect |
| 5. C5×#1132 | C2 | semidirect |
| 6. #10587845 | C2 | semidirect |
| 7. #10587844 | C2 | semidirect |
| 11. C7×Dic10 | C22 | semidirect |
| 13. C5×Dic14 | C22 | semidirect |
| 17. C5×C7×C8 | C22 | semidirect |
| 18. C7⋊#168 | C22 | semidirect |
| 34. #1132 | D5 | semidirect |
| 41. #677 | D7 | semidirect |
| 44. D35 | SD16 | semidirect |
| 55. Dic14 | C2×D5 | semidirect |
| 56. C7×C8 | C2×D5 | semidirect |
| 66. Dic10 | C2×D7 | semidirect |
| 67. C5×C8 | C2×D7 | semidirect |
| 69. C5×C7 | C2×SD16 | semidirect |
| 112. C8 | D5×D7 | 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 |
|---|---|
| #10587950 | 2 |
| D35⋊Q8 | 2 |
| C8×D35 | 2 |
| C7×#677 | 2 |
| C5×#1132 | 2 |
| #10587845 | 2 |
| #10587844 | 2 |
| D7×SD16 | 5 |
| D5×SD16 | 7 |