Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
188 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 1. C2×C5×C7×D4 | C2 | semidirect |
| 2. C2×C7×C22⋊D5 | C2 | semidirect |
| 3. C2×C7×C22⋊D5 | C2 | semidirect |
| 4. C22×C7×Dic5 | C2 | semidirect |
| 5. C7×C22⋊Dic5 | C2 | semidirect |
| 6. C7×#685 | C2 | semidirect |
| 7. C7×#683 | C2 | semidirect |
| 20. #4085 | C7 | direct (N × H) |
| 26. C22×C5×C7 | D4 | semidirect |
| 34. C7×Dic5 | D4 | semidirect |
| 37. C2×C7×D4 | D5 | semidirect |
| 42. C2×C5×D4 | C2×C7 | semidirect |
| 43. C2×C22⋊D5 | C2×C7 | semidirect |
| 44. C2×C22⋊D5 | C2×C7 | semidirect |
| 45. C22×Dic5 | C2×C7 | semidirect |
| 46. C22⋊Dic5 | C2×C7 | semidirect |
| 47. #685 | C2×C7 | semidirect |
| 48. #683 | C2×C7 | semidirect |
| 77. C5×C7 | #121 | semidirect |
| 87. C22×C7 | C22⋊D5 | semidirect |
| 98. C22×C5 | C7×D4 | semidirect |
| 106. Dic5 | C7×D4 | semidirect |
| 109. C2×D4 | C7×D5 | semidirect |
| 137. C7 | #4085 | direct (N × H) |
| 138. C5 | C7×#121 | semidirect |
| 147. C22 | C7×C22⋊D5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C7×D4 | 2 |
| C2×C7×C22⋊D5 | 2 |
| C22×C7×Dic5 | 2 |
| C7×C22⋊Dic5 | 2 |
| C7×#685 | 2 |
| C7×#683 | 2 |
| C7×#121 | 5 |
| #4085 | 7 |