Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
120 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 120 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×C7×Dic6 | C2 | semidirect |
| 3. C3×C7×M16 | C2 | semidirect |
| 4. C7×Dic12 | C2 | semidirect |
| 5. C7×#204 | C2 | semidirect |
| 20. C7×M16 | D3 | semidirect |
| 21. #909 | C7 | direct (N × H) |
| 38. C2×Dic6 | C2×C7 | semidirect |
| 39. C3×M16 | C2×C7 | semidirect |
| 40. Dic12 | C2×C7 | semidirect |
| 41. #204 | C2×C7 | semidirect |
| 61. C3×C7 | #137 | semidirect |
| 66. M16 | D3×C7 | semidirect |
| 85. C7 | #909 | direct (N × H) |
| 95. C3 | C7×#137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#235 | 2 |
| C2×C7×Dic6 | 2 |
| C3×C7×M16 | 2 |
| C7×Dic12 | 2 |
| C7×#204 | 2 |
| C7×#137 | 3 |
| #909 | 7 |