Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 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. C7×Dic3⋊C4 | C2 | semidirect |
| 3. C3×C4×Dic7 | C2 | semidirect |
| 4. Dic3⋊Dic7 | C2 | semidirect |
| 5. #66577 | C2 | semidirect |
| 22. C4×Dic7 | D3 | semidirect |
| 47. Dic3⋊C4 | D7 | semidirect |
| 70. C3×C7 | #126 | semidirect |
| 99. C7 | #876 | semidirect |
| 114. C3 | #6461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66631 | 2 |
| C7×Dic3⋊C4 | 2 |
| C3×C4×Dic7 | 2 |
| Dic3⋊Dic7 | 2 |
| #66577 | 2 |
| #66575 | 2 |
| #6461 | 3 |
| #876 | 7 |