Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
148 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 66 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×C7×Dic6 | C2 | semidirect |
| 3. C3×C7×C4⋊C4 | C2 | semidirect |
| 6. C7×Dic3⋊C4 | C2 | semidirect |
| 7. C7×Dic3⋊C4 | C2 | semidirect |
| 22. C7×C4⋊C4 | D3 | semidirect |
| 25. #896 | C7 | direct (N × H) |
| 29. C2×D3×C7 | Q8 | semidirect |
| 46. C2×Dic6 | C2×C7 | semidirect |
| 47. C3×C4⋊C4 | C2×C7 | semidirect |
| 50. Dic3⋊C4 | C2×C7 | semidirect |
| 51. Dic3⋊C4 | C2×C7 | semidirect |
| 76. C3×C7 | C22⋊Q8 | semidirect |
| 81. C4⋊C4 | D3×C7 | semidirect |
| 91. C2×D3 | C7×Q8 | semidirect |
| 107. C7 | #896 | direct (N × H) |
| 122. C3 | C7×C22⋊Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D3×C7 | 2 |
| C2×C7×Dic6 | 2 |
| C3×C7×C4⋊C4 | 2 |
| C7×(C2×D3)⋊C4 | 2 |
| C7×Dic3⋊C4 | 2 |
| C7×C22⋊Q8 | 3 |
| #896 | 7 |