Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
264 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 114 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. C22×C4×C5×C7 | C2 | semidirect |
| 3. C22×C7×Dic5 | C2 | semidirect |
| 4. C7×#685 | C2 | direct (N × H) |
| 8. C22×C7×D5 | C4 | semidirect |
| 11. C2×C4×C5×C7 | C22 | semidirect |
| 13. C2×C7×Dic5 | C22 | semidirect |
| 15. C2×#685 | C7 | direct (N × H) |
| 23. C2×C7×D5 | C2×C4 | semidirect |
| 28. C22×C4×C7 | D5 | semidirect |
| 31. C22×C4×C5 | C2×C7 | semidirect |
| 32. C22×Dic5 | C2×C7 | semidirect |
| 33. #685 | C2×C7 | direct (N × H) |
| 34. C2×C5×C7 | C22⋊C4 | semidirect |
| 47. C2×C4×C7 | C2×D5 | semidirect |
| 51. C22×D5 | C4×C7 | semidirect |
| 54. C2×C4×C5 | C22×C7 | semidirect |
| 56. C2×Dic5 | C22×C7 | semidirect |
| 57. C5×C7 | C2×C22⋊C4 | semidirect |
| 76. C2×D5 | C2×C4×C7 | semidirect |
| 81. C22×C4 | C7×D5 | semidirect |
| 84. C2×C7 | #685 | direct (N × H) |
| 88. C2×C5 | C7×C22⋊C4 | semidirect |
| 101. C2×C4 | C2×C7×D5 | semidirect |
| 102. C7 | C2×#685 | direct (N × H) |
| 103. C5 | C2×C7×C22⋊C4 | semidirect |
| 115. C2 | C7×#685 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C7×D5 | 2 |
| C22×C4×C5×C7 | 2 |
| C22×C7×Dic5 | 2 |
| C7×#685 | 2 |
| C2×C7×C22⋊C4 | 5 |
| C2×#685 | 7 |