Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
136 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 44 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. D7×Dic6 | C2 | semidirect |
| 3. #66623 | C2 | semidirect |
| 4. C7×#204 | C2 | semidirect |
| 5. C3×C8×D7 | C2 | semidirect |
| 6. #66568 | C2 | semidirect |
| 7. #66567 | C2 | semidirect |
| 11. Dic42 | C22 | semidirect |
| 13. C7×Dic6 | C22 | semidirect |
| 18. C3×C7×C8 | C22 | semidirect |
| 19. C3×C7⋊C8 | C22 | semidirect |
| 26. C8×D7 | D3 | semidirect |
| 45. C7×C8 | C2×D3 | semidirect |
| 46. C7⋊C8 | C2×D3 | semidirect |
| 53. #204 | D7 | direct (N × H) |
| 56. C3×D7 | SD16 | semidirect |
| 75. Dic6 | C2×D7 | semidirect |
| 77. C3×C8 | C2×D7 | semidirect |
| 78. C3×C7 | C2×SD16 | semidirect |
| 89. D7 | #204 | direct (N × H) |
| 108. C8 | D3×D7 | semidirect |
| 109. C7 | C2×#204 | semidirect |
| 122. C3 | D7×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D7×D12 | 2 |
| D7×Dic6 | 2 |
| #66623 | 2 |
| C7×#204 | 2 |
| C3×C8×D7 | 2 |
| #66568 | 2 |
| #66567 | 2 |
| D7×SD16 | 3 |
| C2×#204 | 7 |