Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
184 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 4. #10587900 | C2 | semidirect |
| 5. C7×#683 | C2 | semidirect |
| 6. #10587859 | C2 | semidirect |
| 7. #10587858 | C2 | semidirect |
| 17. D7×Dic5 | C4 | semidirect |
| 26. Dic35 | C2×C4 | semidirect |
| 29. C7×Dic5 | C2×C4 | semidirect |
| 43. #683 | D7 | direct (N × H) |
| 47. C5×D7 | C4⋊C4 | semidirect |
| 68. C5×C7 | C2×C4⋊C4 | semidirect |
| 89. Dic5 | C4×D7 | semidirect |
| 100. D7 | #683 | direct (N × H) |
| 115. C7 | C2×#683 | semidirect |
| 116. C5 | D7×C4⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×D7 | 2 |
| C2×D7×Dic5 | 2 |
| #10587900 | 2 |
| C7×#683 | 2 |
| #10587859 | 2 |
| #10587858 | 2 |
| D7×C4⋊C4 | 5 |
| C2×#683 | 7 |