Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
156 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 66 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. C22×C7×Dic3 | C2 | semidirect |
| 3. C7×#217 | C2 | semidirect |
| 4. C7×#217 | C2 | semidirect |
| 5. C7×Dic3⋊C4 | C2 | semidirect |
| 19. #935 | C7 | direct (N × H) |
| 36. C22×Dic3 | C2×C7 | semidirect |
| 37. #217 | C2×C7 | semidirect |
| 38. #217 | C2×C7 | semidirect |
| 39. Dic3⋊C4 | C2×C7 | semidirect |
| 60. C3×C7 | #123 | semidirect |
| 85. C7 | #935 | direct (N × H) |
| 98. C3 | C7×#123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×D4 | 2 |
| C22×C7×Dic3 | 2 |
| C7×#217 | 2 |
| C7×Dic3⋊C4 | 2 |
| C7×#123 | 3 |
| #935 | 7 |