Finite Group DatabasebetaFinite Group DatabasebetaOrder 1680.
136 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 58 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×C3×C4×C5×C7 | C2 | semidirect |
| 3. C2×C7×Dic15 | C2 | semidirect |
| 8. C2×C7×D15 | C4 | semidirect |
| 13. C2×C4×C5×C7 | D3 | semidirect |
| 15. #6714 | C7 | direct (N × H) |
| 21. C2×C3×C4×C7 | D5 | semidirect |
| 30. C2×C3×C4×C5 | C2×C7 | semidirect |
| 31. C2×Dic15 | C2×C7 | semidirect |
| 33. C3×C5×C7 | C22⋊C4 | semidirect |
| 48. C2×D15 | C4×C7 | semidirect |
| 53. C2×C4×C7 | D15 | semidirect |
| 60. C2×C4×C5 | D3×C7 | semidirect |
| 62. C5×C7 | (C2×D3)⋊C4 | semidirect |
| 74. C2×C3×C4 | C7×D5 | semidirect |
| 76. C3×C7 | #685 | semidirect |
| 84. C3×C5 | C7×C22⋊C4 | semidirect |
| 101. C2×C4 | C7×D15 | semidirect |
| 102. C7 | #6714 | direct (N × H) |
| 107. C5 | C7×(C2×D3)⋊C4 | semidirect |
| 114. C3 | C7×#685 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×D15 | 2 |
| C2×C3×C4×C5×C7 | 2 |
| C2×C7×Dic15 | 2 |
| C7×#685 | 3 |
| C7×(C2×D3)⋊C4 | 5 |
| #6714 | 7 |