Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
152 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 152 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 |
|---|---|---|
| 2. C4×Dic21 | C2 | semidirect |
| 3. C7×Dic3⋊C4 | C2 | semidirect |
| 5. Dic3⋊Dic7 | C2 | semidirect |
| 7. Dic3×Dic7 | C2 | semidirect |
| 16. Dic3×D7 | C4 | semidirect |
| 47. Dic3⋊C4 | D7 | semidirect |
| 73. C3×C7 | #117 | semidirect |
| 103. C7 | #877 | semidirect |
| 118. C3 | #6455 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic3×D7 | 2 |
| C4×Dic21 | 2 |
| C7×Dic3⋊C4 | 2 |
| C3×(C2×D7)⋊C4 | 2 |
| Dic3⋊Dic7 | 2 |
| (C2×D7)⋊Dic3 | 2 |
| Dic3×Dic7 | 2 |
| #6455 | 3 |
| #877 | 7 |