Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
148 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 48 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×#4248 | C2 | semidirect |
| 3. C7×Dic3⋊C4 | C2 | semidirect |
| 4. C3×Dic7⋊C4 | C2 | semidirect |
| 5. #66577 | C2 | semidirect |
| 24. Dic7⋊C4 | D3 | semidirect |
| 29. C2×D21 | Q8 | semidirect |
| 51. Dic3⋊C4 | D7 | semidirect |
| 76. C3×C7 | C22⋊Q8 | semidirect |
| 107. C7 | #896 | semidirect |
| 122. C3 | #6459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D21 | 2 |
| C2×#4248 | 2 |
| C7×Dic3⋊C4 | 2 |
| C3×Dic7⋊C4 | 2 |
| #66577 | 2 |
| #66575 | 2 |
| #6459 | 3 |
| #896 | 7 |