Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
188 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 72 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. C22×C3×Dic7 | C2 | semidirect |
| 3. C2×D3×Dic7 | C2 | semidirect |
| 4. #66636 | C2 | semidirect |
| 5. Dic3⋊Dic7 | C2 | semidirect |
| 6. (C2×D3)⋊Dic7 | C2 | semidirect |
| 7. Dic3×Dic7 | C2 | semidirect |
| 13. C7×#67 | C4 | semidirect |
| 21. C22×Dic7 | D3 | semidirect |
| 29. C22×C3×C7 | C2×C4 | semidirect |
| 33. C2×D3×C7 | C2×C4 | semidirect |
| 37. C3×Dic7 | D4 | semidirect |
| 38. C7×Dic3 | C2×C4 | semidirect |
| 67. C22×C7 | C4×D3 | semidirect |
| 73. Dic7 | #67 | direct (N × H) |
| 79. #67 | Dic7 | direct (N × H) |
| 84. C3×C7 | C4×D4 | semidirect |
| 99. C22×C3 | C2×Dic7 | semidirect |
| 103. C2×D3 | C2×Dic7 | semidirect |
| 108. Dic3 | C2×Dic7 | semidirect |
| 119. C7 | C4×#67 | semidirect |
| 130. C22 | D3×Dic7 | semidirect |
| 137. C3 | D4×Dic7 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#67 | 2 |
| C22×C3×Dic7 | 2 |
| C2×D3×Dic7 | 2 |
| #66636 | 2 |
| Dic3⋊Dic7 | 2 |
| (C2×D3)⋊Dic7 | 2 |
| Dic3×Dic7 | 2 |
| D4×Dic7 | 3 |
| C4×#67 | 7 |