Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
120 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 47 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. C2×Dic42 | C2 | semidirect |
| 3. C3×C7×M16 | C2 | semidirect |
| 4. Dic84 | C2 | semidirect |
| 5. #66623 | C2 | semidirect |
| 18. C7×M16 | D3 | semidirect |
| 39. C3×M16 | D7 | semidirect |
| 61. C3×C7 | #137 | semidirect |
| 66. M16 | D21 | semidirect |
| 85. C7 | #909 | semidirect |
| 95. C3 | #6472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66728 | 2 |
| C2×Dic42 | 2 |
| C3×C7×M16 | 2 |
| Dic84 | 2 |
| #66623 | 2 |
| #6472 | 3 |
| #909 | 7 |