Finite Group DatabasebetaFinite Group DatabasebetaOrder 1680.
152 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 72 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. C3×Dic70 | C2 | semidirect |
| 2. C3×C7×Dic10 | C2 | semidirect |
| 4. C3×#63308 | C2 | semidirect |
| 6. D7×Dic10 | C3 | direct (N × H) |
| 13. Dic70 | C2×C3 | semidirect |
| 14. C7×Dic10 | C2×C3 | semidirect |
| 16. #63308 | C2×C3 | semidirect |
| 20. C3×C5×D7 | Q8 | semidirect |
| 35. C3×Dic10 | D7 | direct (N × H) |
| 37. C3×C5×C7 | C2×Q8 | semidirect |
| 45. C5×D7 | C3×Q8 | semidirect |
| 58. C3×D7 | Dic10 | direct (N × H) |
| 63. Dic10 | C3×D7 | direct (N × H) |
| 64. C5×C7 | C2×C3×Q8 | semidirect |
| 77. C3×C7 | C2×Dic10 | semidirect |
| 84. C3×C5 | Q8×D7 | semidirect |
| 86. D7 | C3×Dic10 | direct (N × H) |
| 99. C7 | C2×C3×Dic10 | semidirect |
| 102. C5 | C3×Q8×D7 | semidirect |
| 108. C3 | D7×Dic10 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Dic70 | 2 |
| C3×C7×Dic10 | 2 |
| C3×C4×C5×D7 | 2 |
| C3×#63308 | 2 |
| C3×D7×Dic5 | 2 |
| D7×Dic10 | 3 |
| C3×Q8×D7 | 5 |
| C2×C3×Dic10 | 7 |