Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
152 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 62 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. C2×C7×Dic10 | C2 | semidirect |
| 3. C5×C7×C22⋊C4 | C2 | semidirect |
| 4. C7×C22⋊Dic5 | C2 | semidirect |
| 5. C7×#685 | C2 | semidirect |
| 6. C7×#685 | C2 | semidirect |
| 7. C4×C7×Dic5 | C2 | semidirect |
| 18. #4031 | C7 | direct (N × H) |
| 36. C7×C22⋊C4 | D5 | semidirect |
| 39. C2×Dic10 | C2×C7 | semidirect |
| 40. C5×C22⋊C4 | C2×C7 | semidirect |
| 41. C22⋊Dic5 | C2×C7 | semidirect |
| 42. #685 | C2×C7 | semidirect |
| 43. #685 | C2×C7 | semidirect |
| 44. C4×Dic5 | C2×C7 | semidirect |
| 68. C5×C7 | #124 | semidirect |
| 99. C22⋊C4 | C7×D5 | semidirect |
| 120. C7 | #4031 | direct (N × H) |
| 121. C5 | C7×#124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×C22⋊D5 | 2 |
| C2×C7×Dic10 | 2 |
| C5×C7×C22⋊C4 | 2 |
| C7×C22⋊Dic5 | 2 |
| C7×#685 | 2 |
| C4×C7×Dic5 | 2 |
| C7×#124 | 5 |
| #4031 | 7 |