Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
156 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 156 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. C22×C3×Dic7 | C2 | semidirect |
| 3. C3×C7×C22⋊C4 | C2 | semidirect |
| 4. C3×(C2×D7)⋊C4 | C2 | semidirect |
| 5. C3×C4⋊Dic7 | C2 | semidirect |
| 6. #6449 | C3 | direct (N × H) |
| 15. C22×Dic7 | C2×C3 | semidirect |
| 16. C7×C22⋊C4 | C2×C3 | semidirect |
| 17. (C2×D7)⋊C4 | C2×C3 | semidirect |
| 18. C4⋊Dic7 | C2×C3 | semidirect |
| 39. C3×C22⋊C4 | D7 | semidirect |
| 60. C3×C7 | #123 | semidirect |
| 65. C22⋊C4 | C3×D7 | semidirect |
| 85. C7 | C3×#123 | semidirect |
| 98. C3 | #6449 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C22⋊D7 | 2 |
| C22×C3×Dic7 | 2 |
| C3×C7×C22⋊C4 | 2 |
| C3×(C2×D7)⋊C4 | 2 |
| C3×C4⋊Dic7 | 2 |
| #6449 | 3 |
| C3×#123 | 7 |