Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
188 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 72 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. C22×C7×Dic3 | C2 | semidirect |
| 3. C2×Dic3×D7 | C2 | semidirect |
| 4. #66636 | C2 | semidirect |
| 5. Dic7⋊Dic3 | C2 | semidirect |
| 6. (C2×D7)⋊Dic3 | C2 | semidirect |
| 7. Dic3×Dic7 | C2 | semidirect |
| 16. C3×C22⋊D7 | C4 | semidirect |
| 29. C22×C3×C7 | C2×C4 | semidirect |
| 33. C2×C3×D7 | C2×C4 | semidirect |
| 36. C3×Dic7 | C2×C4 | semidirect |
| 38. C7×Dic3 | D4 | semidirect |
| 44. C22⋊D7 | Dic3 | direct (N × H) |
| 51. C22×Dic3 | D7 | semidirect |
| 64. C22×C7 | C2×Dic3 | semidirect |
| 68. C2×D7 | C2×Dic3 | semidirect |
| 73. Dic7 | C2×Dic3 | semidirect |
| 84. C3×C7 | C4×D4 | semidirect |
| 102. C22×C3 | C4×D7 | semidirect |
| 108. Dic3 | C22⋊D7 | direct (N × H) |
| 119. C7 | D4×Dic3 | semidirect |
| 130. C22 | Dic3×D7 | semidirect |
| 137. C3 | C4×C22⋊D7 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×Dic3 | 2 |
| C2×C3×C22⋊D7 | 2 |
| C2×Dic3×D7 | 2 |
| #66636 | 2 |
| Dic7⋊Dic3 | 2 |
| (C2×D7)⋊Dic3 | 2 |
| Dic3×Dic7 | 2 |
| C4×C22⋊D7 | 3 |
| D4×Dic3 | 7 |