Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
148 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 70 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×C3×Dic14 | C2 | semidirect |
| 3. C3×C7×C4⋊C4 | C2 | semidirect |
| 5. C3×C4⋊Dic7 | C2 | semidirect |
| 6. #6460 | C3 | direct (N × H) |
| 15. C2×Dic14 | C2×C3 | semidirect |
| 16. C7×C4⋊C4 | C2×C3 | semidirect |
| 18. C4⋊Dic7 | C2×C3 | semidirect |
| 23. C2×C3×D7 | Q8 | semidirect |
| 38. C3×C4⋊C4 | D7 | semidirect |
| 48. C2×D7 | C3×Q8 | semidirect |
| 60. C3×C7 | C22⋊Q8 | semidirect |
| 64. C4⋊C4 | C3×D7 | semidirect |
| 85. C7 | C3×C22⋊Q8 | semidirect |
| 98. C3 | #6460 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D7 | 2 |
| C2×C3×Dic14 | 2 |
| C3×C7×C4⋊C4 | 2 |
| C3×(C2×D7)⋊C4 | 2 |
| C3×C4⋊Dic7 | 2 |
| #6460 | 3 |
| C3×C22⋊Q8 | 7 |