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 |
|---|---|---|
| 1. C3×D4×D7 | C2 | semidirect |
| 2. #66677 | C2 | semidirect |
| 3. #66632 | C2 | semidirect |
| 4. C7×#214 | C2 | semidirect |
| 5. #66563 | C2 | semidirect |
| 6. #66561 | C2 | semidirect |
| 7. #66557 | C2 | semidirect |
| 11. D84 | C22 | semidirect |
| 12. C7×Dic6 | C22 | semidirect |
| 18. C3⋊(C7⋊C8) | C22 | semidirect |
| 19. C7×C3⋊C8 | C22 | semidirect |
| 21. D4×D7 | D3 | semidirect |
| 50. #214 | D7 | semidirect |
| 76. Dic6 | C2×D7 | semidirect |
| 78. C3⋊C8 | C2×D7 | semidirect |
| 79. C3×C7 | AGL(1,ℤ/8) | semidirect |
| 111. C7 | #932 | semidirect |
| 125. C3 | #6477 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D4×D7 | 2 |
| #66677 | 2 |
| #66632 | 2 |
| C7×#214 | 2 |
| #66563 | 2 |
| #66561 | 2 |
| #66557 | 2 |
| #6477 | 3 |
| #932 | 7 |