Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
156 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 62 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×C4×D3×C7 | C2 | semidirect |
| 3. C3×C7×C4⋊C4 | C2 | semidirect |
| 4. C7×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C7×(C2×D3)⋊C4 | C2 | semidirect |
| 6. C7×(C2×D3)⋊C4 | C2 | semidirect |
| 7. C7×Dic3⋊C4 | C2 | semidirect |
| 21. C7×C4⋊C4 | D3 | semidirect |
| 25. #894 | C7 | direct (N × H) |
| 48. C2×C4×D3 | C2×C7 | semidirect |
| 49. C3×C4⋊C4 | C2×C7 | semidirect |
| 50. (C2×D3)⋊C4 | C2×C7 | semidirect |
| 51. (C2×D3)⋊C4 | C2×C7 | semidirect |
| 52. (C2×D3)⋊C4 | C2×C7 | semidirect |
| 53. Dic3⋊C4 | C2×C7 | semidirect |
| 81. C3×C7 | #123 | semidirect |
| 85. C4⋊C4 | D3×C7 | semidirect |
| 115. C7 | #894 | direct (N × H) |
| 133. C3 | C7×#123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×D12 | 2 |
| C2×C4×D3×C7 | 2 |
| C3×C7×C4⋊C4 | 2 |
| C7×(C2×D3)⋊C4 | 2 |
| C7×Dic3⋊C4 | 2 |
| C7×#123 | 3 |
| #894 | 7 |