Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
264 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 98 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×C4×C5×D7 | C2 | semidirect |
| 3. C5×C7×C22⋊C4 | C2 | semidirect |
| 4. C5×C22⋊Dic7 | C2 | semidirect |
| 5. C5×(C2×D7)⋊C4 | C2 | semidirect |
| 8. C22×C5×D7 | C4 | semidirect |
| 11. C2×C4×C5×C7 | C22 | semidirect |
| 12. C2×C5×Dic7 | C22 | semidirect |
| 14. D7×C22⋊C4 | C5 | direct (N × H) |
| 17. C22×C5×C7 | C2×C4 | semidirect |
| 22. C2×C5×D7 | C2×C4 | semidirect |
| 27. C2×C4×D7 | C2×C5 | semidirect |
| 28. C7×C22⋊C4 | C2×C5 | semidirect |
| 29. C22⋊Dic7 | C2×C5 | semidirect |
| 30. (C2×D7)⋊C4 | C2×C5 | semidirect |
| 35. C5×C22⋊C4 | D7 | direct (N × H) |
| 40. C5×D7 | C22⋊C4 | direct (N × H) |
| 43. C22×D7 | C4×C5 | semidirect |
| 46. 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 |
| 60. C22×C7 | C2×C4×C5 | semidirect |
| 65. C2×D7 | C2×C4×C5 | semidirect |
| 75. C22×C5 | C4×D7 | semidirect |
| 83. C22⋊C4 | C5×D7 | direct (N × H) |
| 88. D7 | C5×C22⋊C4 | direct (N × H) |
| 101. C2×C4 | C2×C5×D7 | semidirect |
| 102. C7 | C2×C5×C22⋊C4 | semidirect |
| 103. C5 | D7×C22⋊C4 | direct (N × H) |
| 110. C22 | C4×C5×D7 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C5×D7 | 2 |
| C2×C4×C5×D7 | 2 |
| C5×C7×C22⋊C4 | 2 |
| C5×C22⋊Dic7 | 2 |
| C5×(C2×D7)⋊C4 | 2 |
| D7×C22⋊C4 | 5 |
| C2×C5×C22⋊C4 | 7 |