Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
188 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 60 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×C4×D21 | C2 | semidirect |
| 3. C2×Dic3×D7 | C2 | semidirect |
| 4. C7×Dic3⋊C4 | C2 | semidirect |
| 5. C3×(C2×D7)⋊C4 | C2 | semidirect |
| 6. #66575 | C2 | semidirect |
| 7. Dic3×Dic7 | C2 | semidirect |
| 17. #4246 | C4 | semidirect |
| 24. (C2×D7)⋊C4 | D3 | semidirect |
| 30. C2×D21 | C2×C4 | semidirect |
| 33. C2×C3×D7 | C2×C4 | semidirect |
| 35. Dic21 | D4 | semidirect |
| 38. C7×Dic3 | C2×C4 | semidirect |
| 54. Dic3⋊C4 | D7 | semidirect |
| 68. C2×D7 | C4×D3 | semidirect |
| 84. C3×C7 | C4×D4 | semidirect |
| 108. Dic3 | C4×D7 | semidirect |
| 119. C7 | #67⋊C4 | semidirect |
| 137. C3 | #6456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D21 | 2 |
| C2×#4246 | 2 |
| C2×Dic3×D7 | 2 |
| C7×Dic3⋊C4 | 2 |
| C3×(C2×D7)⋊C4 | 2 |
| #66575 | 2 |
| Dic3×Dic7 | 2 |
| #6456 | 3 |
| #67⋊C4 | 7 |