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. C5×Dic42 | C2 | semidirect |
| 2. C5×C7×Dic6 | C2 | semidirect |
| 4. C5×#4248 | C2 | semidirect |
| 12. D7×Dic6 | C5 | direct (N × H) |
| 20. C3×C5×D7 | Q8 | semidirect |
| 21. Dic42 | C2×C5 | semidirect |
| 22. C7×Dic6 | C2×C5 | semidirect |
| 24. #4248 | C2×C5 | semidirect |
| 35. C5×Dic6 | D7 | direct (N × H) |
| 37. C3×C5×C7 | C2×Q8 | semidirect |
| 45. C5×D7 | Dic6 | direct (N × H) |
| 58. C3×D7 | C5×Q8 | semidirect |
| 64. C5×C7 | C2×Dic6 | semidirect |
| 76. Dic6 | C5×D7 | direct (N × H) |
| 77. C3×C7 | C2×C5×Q8 | semidirect |
| 84. C3×C5 | Q8×D7 | semidirect |
| 86. D7 | C5×Dic6 | direct (N × H) |
| 99. C7 | C2×C5×Dic6 | semidirect |
| 102. C5 | D7×Dic6 | direct (N × H) |
| 108. C3 | C5×Q8×D7 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Dic42 | 2 |
| C5×C7×Dic6 | 2 |
| C3×C4×C5×D7 | 2 |
| C5×#4248 | 2 |
| C5×Dic3×D7 | 2 |
| C5×Q8×D7 | 3 |
| D7×Dic6 | 5 |
| C2×C5×Dic6 | 7 |