Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
136 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 50 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. D5⋊(C7⋊C8) | C2 | semidirect |
| 3. C7×D5⋊C8 | C2 | semidirect |
| 4. #10587922 | C2 | semidirect |
| 5. #10587921 | C2 | semidirect |
| 13. C7⋊#170 | C22 | semidirect |
| 14. C7×#170 | C22 | semidirect |
| 34. D5⋊C8 | D7 | semidirect |
| 38. C7×D5 | M16 | semidirect |
| 56. #170 | C2×D7 | semidirect |
| 57. C5×C7 | C2×M16 | semidirect |
| 87. D5 | #1131 | semidirect |
| 97. C7 | D5⋊M16 | semidirect |
| 98. C5 | C2×#1131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D5×D7 | 2 |
| D5⋊(C7⋊C8) | 2 |
| C7×D5⋊C8 | 2 |
| #10587922 | 2 |
| #10587921 | 2 |
| C2×#1131 | 5 |
| D5⋊M16 | 7 |