Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
152 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 152 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 |
|---|---|---|
| 1. C2×C3×C7×D4 | C2 | semidirect |
| 2. C2×C7×D12 | C2 | semidirect |
| 3. C7×#213 | C2 | direct (N × H) |
| 4. C2×C7×C3⋊C8 | C2 | semidirect |
| 9. C3×C7×D4 | C22 | semidirect |
| 12. C7×D12 | C22 | semidirect |
| 13. C7×C3⋊C8 | C22 | semidirect |
| 15. C2×C7×D4 | D3 | semidirect |
| 18. C2×#213 | C7 | direct (N × H) |
| 31. C7×D4 | C2×D3 | semidirect |
| 34. C2×C3×D4 | C2×C7 | semidirect |
| 35. C2×D12 | C2×C7 | semidirect |
| 36. #213 | C2×C7 | direct (N × H) |
| 37. C2×C3⋊C8 | C2×C7 | semidirect |
| 39. C2×C3×C7 | D8 | semidirect |
| 53. C3×D4 | C22×C7 | semidirect |
| 56. D12 | C22×C7 | semidirect |
| 57. C3⋊C8 | C22×C7 | semidirect |
| 58. C3×C7 | C2×D8 | semidirect |
| 60. C2×D4 | D3×C7 | semidirect |
| 65. C2×C7 | #213 | direct (N × H) |
| 79. D4 | C2×D3×C7 | semidirect |
| 82. C7 | C2×#213 | direct (N × H) |
| 84. C2×C3 | C7×D8 | semidirect |
| 94. C3 | C2×C7×D8 | semidirect |
| 97. C2 | C7×#213 | direct (N × H) |
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×D12 | 2 |
| C7×#213 | 2 |
| C2×C7×C3⋊C8 | 2 |
| C2×C7×D8 | 3 |
| C2×#213 | 7 |