Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
148 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 50 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 |
|---|---|---|
| 1. C2×#4248 | C2 | semidirect |
| 3. #66629 | C2 | semidirect |
| 4. C7×C4⋊Dic3 | C2 | semidirect |
| 6. #66577 | C2 | semidirect |
| 29. C2×C3×D7 | Q8 | semidirect |
| 49. C4⋊Dic3 | D7 | semidirect |
| 60. C2×D7 | Dic6 | semidirect |
| 76. C3×C7 | C22⋊Q8 | semidirect |
| 107. C7 | #878 | 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×#4248 | 2 |
| C2×Dic3×D7 | 2 |
| #66629 | 2 |
| C7×C4⋊Dic3 | 2 |
| C3×(C2×D7)⋊C4 | 2 |
| #66577 | 2 |
| (C2×D7)⋊Dic3 | 2 |
| #6459 | 3 |
| #878 | 7 |