Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
188 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 71 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. C2×C4×D21 | C2 | semidirect |
| 4. #66636 | C2 | semidirect |
| 5. #66631 | C2 | semidirect |
| 6. #66629 | C2 | semidirect |
| 7. C4×Dic21 | C2 | semidirect |
| 14. #4268 | C4 | direct (N × H) |
| 19. C22×C4×C7 | D3 | semidirect |
| 29. C22×C3×C7 | C2×C4 | semidirect |
| 33. C2×D21 | C2×C4 | semidirect |
| 35. C3×C4×C7 | D4 | semidirect |
| 38. Dic21 | C2×C4 | semidirect |
| 49. C22×C3×C4 | D7 | semidirect |
| 64. C22×C7 | C4×D3 | semidirect |
| 70. C4×C7 | #67 | semidirect |
| 84. C3×C7 | C4×D4 | semidirect |
| 87. C22×C4 | D21 | semidirect |
| 99. C22×C3 | C4×D7 | semidirect |
| 105. C3×C4 | C22⋊D7 | semidirect |
| 119. C7 | C4×#67 | semidirect |
| 130. C22 | C4×D21 | semidirect |
| 136. C4 | #4268 | direct (N × H) |
| 137. C3 | C4×C22⋊D7 | 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×#4268 | 2 |
| C2×C4×D21 | 2 |
| #66636 | 2 |
| #66631 | 2 |
| #66629 | 2 |
| C4×Dic21 | 2 |
| C4×C22⋊D7 | 3 |
| C4×#67 | 7 |