Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
188 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 188 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 |
|---|---|---|
| 1. C2×C3×C7×D4 | C2 | semidirect |
| 2. C2×C7×#67 | C2 | semidirect |
| 3. C2×C7×#67 | C2 | semidirect |
| 4. C22×C7×Dic3 | C2 | semidirect |
| 5. C7×#217 | C2 | semidirect |
| 6. C7×(C2×D3)⋊C4 | C2 | semidirect |
| 7. C7×Dic3⋊C4 | C2 | semidirect |
| 22. C2×C7×D4 | D3 | semidirect |
| 27. #939 | C7 | direct (N × H) |
| 33. C22×C3×C7 | D4 | semidirect |
| 41. C7×Dic3 | D4 | semidirect |
| 53. C2×C3×D4 | C2×C7 | semidirect |
| 54. C2×#67 | C2×C7 | semidirect |
| 55. C2×#67 | C2×C7 | semidirect |
| 56. C22×Dic3 | C2×C7 | semidirect |
| 57. #217 | C2×C7 | semidirect |
| 58. (C2×D3)⋊C4 | C2×C7 | semidirect |
| 59. Dic3⋊C4 | C2×C7 | semidirect |
| 75. C22×C7 | #67 | semidirect |
| 92. C3×C7 | #121 | semidirect |
| 95. C2×D4 | D3×C7 | semidirect |
| 111. C22×C3 | C7×D4 | semidirect |
| 119. Dic3 | C7×D4 | semidirect |
| 131. C7 | #939 | direct (N × H) |
| 146. C22 | C7×#67 | semidirect |
| 152. C3 | C7×#121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×D4 | 2 |
| C2×C7×#67 | 2 |
| C22×C7×Dic3 | 2 |
| C7×#217 | 2 |
| C7×(C2×D3)⋊C4 | 2 |
| C7×Dic3⋊C4 | 2 |
| C7×#121 | 3 |
| #939 | 7 |