Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
188 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 64 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×D21⋊C4 | C2 | semidirect |
| 4. C7×#217 | C2 | semidirect |
| 5. #66577 | C2 | semidirect |
| 6. #66575 | C2 | semidirect |
| 7. Dic3×Dic7 | C2 | semidirect |
| 11. #4268 | C4 | semidirect |
| 20. C22×Dic7 | D3 | semidirect |
| 29. C22×C3×C7 | C2×C4 | semidirect |
| 33. C2×D21 | C2×C4 | semidirect |
| 34. Dic21 | C2×C4 | semidirect |
| 36. C3×Dic7 | D4 | semidirect |
| 52. #217 | D7 | semidirect |
| 64. C22×C7 | C4×D3 | semidirect |
| 73. Dic7 | #67 | semidirect |
| 84. C3×C7 | C4×D4 | semidirect |
| 99. C22×C3 | C4×D7 | semidirect |
| 119. C7 | C4×#67 | semidirect |
| 130. C22 | D21⋊C4 | semidirect |
| 137. C3 | (C22⋊D7)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4268 | 2 |
| C22×C3×Dic7 | 2 |
| C2×D21⋊C4 | 2 |
| C7×#217 | 2 |
| #66577 | 2 |
| #66575 | 2 |
| Dic3×Dic7 | 2 |
| (C22⋊D7)⋊C4 | 3 |
| C4×#67 | 7 |