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 |
|---|---|---|
| 1. C2×C3×C4×D7 | C2 | semidirect |
| 3. #66629 | C2 | semidirect |
| 4. C7×(C2×D3)⋊C4 | C2 | semidirect |
| 5. Dic3⋊Dic7 | C2 | semidirect |
| 6. (C2×D3)⋊Dic7 | C2 | semidirect |
| 7. (C2×D7)⋊Dic3 | C2 | semidirect |
| 19. C2×C4×D7 | D3 | semidirect |
| 51. (C2×D3)⋊C4 | D7 | semidirect |
| 81. C3×C7 | #123 | semidirect |
| 115. C7 | #929 | semidirect |
| 133. C3 | #6446 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D7 | 2 |
| C2×#4245 | 2 |
| #66629 | 2 |
| C7×(C2×D3)⋊C4 | 2 |
| Dic3⋊Dic7 | 2 |
| (C2×D3)⋊Dic7 | 2 |
| (C2×D7)⋊Dic3 | 2 |
| #6446 | 3 |
| #929 | 7 |