Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
328 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 178 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. C22×C4×C5×C7 | C2 | semidirect |
| 2. C2×C7×C22⋊D5 | C2 | semidirect |
| 3. C7×#709 | C2 | direct (N × H) |
| 4. C2×C7×D20 | C2 | semidirect |
| 5. C2×C4×C7×D5 | C2 | semidirect |
| 6. C2×C7×Dic10 | C2 | semidirect |
| 11. C2×C4×C5×C7 | C22 | semidirect |
| 12. C7×C22⋊D5 | C22 | semidirect |
| 14. C7×D20 | C22 | semidirect |
| 15. C4×C7×D5 | C22 | semidirect |
| 16. C7×Dic10 | C22 | semidirect |
| 18. C2×#709 | C7 | direct (N × H) |
| 32. C22×C4×C7 | D5 | semidirect |
| 33. C22×C4×C5 | C2×C7 | semidirect |
| 34. C2×C22⋊D5 | C2×C7 | semidirect |
| 35. #709 | C2×C7 | direct (N × H) |
| 36. C2×D20 | C2×C7 | semidirect |
| 37. C2×C4×D5 | C2×C7 | semidirect |
| 38. C2×Dic10 | C2×C7 | semidirect |
| 40. C2×C5×C7 | #41 | semidirect |
| 52. C2×C4×C7 | C2×D5 | semidirect |
| 57. C2×C4×C5 | C22×C7 | semidirect |
| 58. C22⋊D5 | C22×C7 | semidirect |
| 60. D20 | C22×C7 | semidirect |
| 61. C4×D5 | C22×C7 | semidirect |
| 62. Dic10 | C22×C7 | semidirect |
| 63. C5×C7 | C2×#41 | semidirect |
| 86. C22×C4 | C7×D5 | semidirect |
| 89. C2×C7 | #709 | direct (N × H) |
| 92. C2×C5 | C7×#41 | semidirect |
| 104. C2×C4 | C2×C7×D5 | semidirect |
| 105. C7 | C2×#709 | direct (N × H) |
| 106. C5 | C2×C7×#41 | semidirect |
| 117. C2 | C7×#709 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×C7 | 2 |
| C2×C7×C22⋊D5 | 2 |
| C7×#709 | 2 |
| C2×C7×D20 | 2 |
| C2×C4×C7×D5 | 2 |
| C2×C7×Dic10 | 2 |
| C2×C7×#41 | 5 |
| C2×#709 | 7 |