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 |
|---|---|---|
| 1. C22×C3×C4×C7 | C2 | semidirect |
| 3. C7×#217 | C2 | semidirect |
| 4. C7×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C7×Dic3⋊C4 | C2 | semidirect |
| 15. C22×C4×C7 | D3 | semidirect |
| 19. #929 | C7 | direct (N × H) |
| 35. C22×C3×C4 | C2×C7 | semidirect |
| 37. #217 | C2×C7 | semidirect |
| 38. (C2×D3)⋊C4 | C2×C7 | semidirect |
| 39. Dic3⋊C4 | C2×C7 | semidirect |
| 60. C3×C7 | #123 | semidirect |
| 62. C22×C4 | D3×C7 | semidirect |
| 85. C7 | #929 | 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 |
|---|---|
| C22×C3×C4×C7 | 2 |
| C2×C7×#67 | 2 |
| C7×#217 | 2 |
| C7×(C2×D3)⋊C4 | 2 |
| C7×Dic3⋊C4 | 2 |
| C7×#123 | 3 |
| #929 | 7 |