Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
136 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 38 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. D4×D21 | C2 | semidirect |
| 2. #66672 | C2 | semidirect |
| 3. C7×#213 | C2 | semidirect |
| 4. C3×#1142 | C2 | semidirect |
| 5. #66566 | C2 | semidirect |
| 6. #66562 | C2 | semidirect |
| 7. #66559 | C2 | semidirect |
| 14. C7×D12 | C22 | semidirect |
| 15. C3×Dic14 | C22 | semidirect |
| 18. C3×C7⋊C8 | C22 | semidirect |
| 19. C7×C3⋊C8 | C22 | semidirect |
| 23. #1142 | D3 | semidirect |
| 44. Dic14 | C2×D3 | semidirect |
| 46. C7⋊C8 | C2×D3 | semidirect |
| 51. #213 | D7 | semidirect |
| 74. D12 | C2×D7 | semidirect |
| 78. C3⋊C8 | C2×D7 | semidirect |
| 79. C3×C7 | AGL(1,ℤ/8) | semidirect |
| 111. C7 | #914 | semidirect |
| 125. C3 | #6474 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D21 | 2 |
| #66672 | 2 |
| C7×#213 | 2 |
| C3×#1142 | 2 |
| #66566 | 2 |
| #66562 | 2 |
| #66559 | 2 |
| #6474 | 3 |
| #914 | 7 |