Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
136 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 136 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 |
|---|---|---|
| 2. D7×Dic10 | C2 | semidirect |
| 3. #10587894 | C2 | semidirect |
| 4. C7×#677 | C2 | semidirect |
| 5. C5×C8×D7 | C2 | semidirect |
| 6. #10587849 | C2 | semidirect |
| 7. #10587848 | C2 | semidirect |
| 10. Dic70 | C22 | semidirect |
| 12. C7×Dic10 | C22 | semidirect |
| 17. C5×C7×C8 | C22 | semidirect |
| 18. C5×C7⋊C8 | C22 | semidirect |
| 35. C8×D7 | D5 | semidirect |
| 42. #677 | D7 | direct (N × H) |
| 45. C5×D7 | SD16 | semidirect |
| 56. C7×C8 | C2×D5 | semidirect |
| 57. C7⋊C8 | C2×D5 | semidirect |
| 66. Dic10 | C2×D7 | semidirect |
| 68. C5×C8 | C2×D7 | semidirect |
| 69. C5×C7 | C2×SD16 | semidirect |
| 97. D7 | #677 | direct (N × H) |
| 112. C8 | D5×D7 | semidirect |
| 113. C7 | C2×#677 | 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 |
|---|---|
| D7×D20 | 2 |
| D7×Dic10 | 2 |
| #10587894 | 2 |
| C7×#677 | 2 |
| C5×C8×D7 | 2 |
| #10587849 | 2 |
| #10587848 | 2 |
| D7×SD16 | 5 |
| C2×#677 | 7 |