Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
120 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 58 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. C3×C7×C4⋊C4 | C2 | semidirect |
| 5. C7×C4⋊Dic3 | C2 | semidirect |
| 6. C7×Dic3⋊C4 | C2 | semidirect |
| 7. C4×C7×Dic3 | C2 | semidirect |
| 18. C7×C4⋊C4 | D3 | semidirect |
| 23. #898 | C7 | direct (N × H) |
| 41. C3×C4⋊C4 | C2×C7 | semidirect |
| 45. C4⋊Dic3 | C2×C7 | semidirect |
| 46. Dic3⋊C4 | C2×C7 | semidirect |
| 47. C4×Dic3 | C2×C7 | semidirect |
| 70. C3×C7 | #126 | semidirect |
| 73. C4⋊C4 | D3×C7 | semidirect |
| 99. C7 | #898 | direct (N × H) |
| 114. C3 | C7×#126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×C4⋊C4 | 2 |
| C7×(C2×D3)⋊C4 | 2 |
| C7×C4⋊Dic3 | 2 |
| C7×Dic3⋊C4 | 2 |
| C4×C7×Dic3 | 2 |
| C7×#126 | 3 |
| #898 | 7 |