Finite Group DatabasebetaFinite Group DatabasebetaOrder 1680.
160 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 70 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. C2×C3×C4×C5×C7 | C2 | semidirect |
| 2. C3×C22⋊D35 | C2 | semidirect |
| 3. C3×D140 | C2 | semidirect |
| 4. C3×C4×D35 | C2 | semidirect |
| 5. C3×Dic70 | C2 | semidirect |
| 6. #10587987 | C3 | direct (N × H) |
| 13. C2×C4×C5×C7 | C2×C3 | semidirect |
| 14. C22⋊D35 | C2×C3 | semidirect |
| 15. D140 | C2×C3 | semidirect |
| 16. C4×D35 | C2×C3 | semidirect |
| 17. Dic70 | C2×C3 | semidirect |
| 22. C2×C3×C4×C7 | D5 | semidirect |
| 32. C2×C3×C4×C5 | D7 | semidirect |
| 38. C3×C5×C7 | #41 | semidirect |
| 53. C2×C4×C7 | C3×D5 | semidirect |
| 62. C2×C4×C5 | C3×D7 | semidirect |
| 67. C5×C7 | C3×#41 | semidirect |
| 80. C2×C3×C4 | D35 | semidirect |
| 81. C3×C7 | #709 | semidirect |
| 88. C3×C5 | #1157 | semidirect |
| 104. C2×C4 | C3×D35 | semidirect |
| 105. C7 | C3×#709 | semidirect |
| 109. C5 | C3×#1157 | semidirect |
| 115. C3 | #10587987 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×C5×C7 | 2 |
| C3×C22⋊D35 | 2 |
| C3×D140 | 2 |
| C3×C4×D35 | 2 |
| C3×Dic70 | 2 |
| #10587987 | 3 |
| C3×#1157 | 5 |
| C3×#709 | 7 |