Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
136 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 40 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. D21⋊Q8 | C2 | semidirect |
| 3. C7×#214 | C2 | semidirect |
| 4. C3×#1142 | C2 | semidirect |
| 5. #66568 | C2 | semidirect |
| 6. #66566 | C2 | semidirect |
| 7. D21⋊C8 | C2 | semidirect |
| 14. C7×Dic6 | C22 | semidirect |
| 15. C3×Dic14 | C22 | semidirect |
| 18. C3×C7⋊C8 | C22 | semidirect |
| 19. C7×C3⋊C8 | C22 | semidirect |
| 24. #1142 | D3 | semidirect |
| 44. Dic14 | C2×D3 | semidirect |
| 46. C7⋊C8 | C2×D3 | semidirect |
| 51. #214 | D7 | semidirect |
| 57. D21 | SD16 | semidirect |
| 75. Dic6 | C2×D7 | semidirect |
| 77. C3⋊C8 | C2×D7 | semidirect |
| 78. C3×C7 | C2×SD16 | semidirect |
| 109. C7 | D3×SD16 | 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 |
|---|---|
| D4×D21 | 2 |
| D21⋊Q8 | 2 |
| C7×#214 | 2 |
| C3×#1142 | 2 |
| #66568 | 2 |
| #66566 | 2 |
| D21⋊C8 | 2 |
| D7×SD16 | 3 |
| D3×SD16 | 7 |