Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
156 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 48 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×D3×Dic7 | C2 | semidirect |
| 3. #66631 | C2 | semidirect |
| 4. C7×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C3×C4⋊Dic7 | C2 | semidirect |
| 6. Dic3⋊Dic7 | C2 | semidirect |
| 7. #66575 | C2 | semidirect |
| 24. C4⋊Dic7 | D3 | semidirect |
| 52. (C2×D3)⋊C4 | D7 | semidirect |
| 81. C3×C7 | #123 | semidirect |
| 115. C7 | #894 | semidirect |
| 133. C3 | #6449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4247 | 2 |
| C2×D3×Dic7 | 2 |
| #66631 | 2 |
| C7×(C2×D3)⋊C4 | 2 |
| C3×C4⋊Dic7 | 2 |
| Dic3⋊Dic7 | 2 |
| #66575 | 2 |
| #6449 | 3 |
| #894 | 7 |