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. D3×C7×D4 | C2 | semidirect |
| 2. #66673 | C2 | semidirect |
| 3. #66632 | C2 | semidirect |
| 4. C3×#1142 | C2 | semidirect |
| 5. #66564 | C2 | semidirect |
| 6. #66562 | C2 | semidirect |
| 7. #66558 | C2 | semidirect |
| 11. D84 | C22 | semidirect |
| 15. C3×Dic14 | C22 | semidirect |
| 18. C3⋊(C7⋊C8) | C22 | semidirect |
| 19. C3×C7⋊C8 | C22 | semidirect |
| 23. #1142 | D3 | semidirect |
| 44. Dic14 | C2×D3 | semidirect |
| 46. C7⋊C8 | C2×D3 | semidirect |
| 48. D3×D4 | D7 | semidirect |
| 79. C3×C7 | AGL(1,ℤ/8) | semidirect |
| 111. C7 | #914 | semidirect |
| 125. C3 | #6495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×C7×D4 | 2 |
| #66673 | 2 |
| #66632 | 2 |
| C3×#1142 | 2 |
| #66564 | 2 |
| #66562 | 2 |
| #66558 | 2 |
| #6495 | 3 |
| #914 | 7 |