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×C5×Dic7 | C2 | semidirect |
| 4. C5×(C2×D7)⋊C4 | C2 | direct (N × H) |
| 8. C22×C5×D7 | C4 | semidirect |
| 11. C2×C4×C5×C7 | C22 | semidirect |
| 13. C2×C5×Dic7 | C22 | semidirect |
| 14. C2×(C2×D7)⋊C4 | C5 | direct (N × H) |
| 23. C2×C5×D7 | C2×C4 | semidirect |
| 27. C22×C4×C7 | C2×C5 | semidirect |
| 28. C22×Dic7 | C2×C5 | semidirect |
| 29. (C2×D7)⋊C4 | C2×C5 | direct (N × H) |
| 32. C22×C4×C5 | D7 | semidirect |
| 34. C2×C5×C7 | C22⋊C4 | semidirect |
| 42. C22×D7 | C4×C5 | semidirect |
| 45. C2×C4×C7 | C22×C5 | semidirect |
| 47. C2×Dic7 | C22×C5 | semidirect |
| 56. C2×C4×C5 | C2×D7 | semidirect |
| 57. C5×C7 | C2×C22⋊C4 | semidirect |
| 66. C2×D7 | C2×C4×C5 | semidirect |
| 81. C22×C4 | C5×D7 | semidirect |
| 83. C2×C7 | C5×C22⋊C4 | semidirect |
| 89. C2×C5 | (C2×D7)⋊C4 | direct (N × H) |
| 101. C2×C4 | C2×C5×D7 | semidirect |
| 102. C7 | C2×C5×C22⋊C4 | semidirect |
| 103. C5 | C2×(C2×D7)⋊C4 | direct (N × H) |
| 115. C2 | C5×(C2×D7)⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C5×D7 | 2 |
| C22×C4×C5×C7 | 2 |
| C22×C5×Dic7 | 2 |
| C5×(C2×D7)⋊C4 | 2 |
| C2×(C2×D7)⋊C4 | 5 |
| C2×C5×C22⋊C4 | 7 |