Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
136 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 57 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. C3×C7×M16 | C2 | semidirect |
| 3. #66627 | C2 | semidirect |
| 4. #66622 | C2 | semidirect |
| 5. C8×D21 | C2 | semidirect |
| 14. C3×C7×C8 | C22 | semidirect |
| 15. C3⋊(C7⋊C8) | C22 | semidirect |
| 17. C7×M16 | D3 | semidirect |
| 37. C7×C8 | C2×D3 | semidirect |
| 40. C3×M16 | D7 | semidirect |
| 47. D21 | M16 | direct (N × H) |
| 64. C3×C8 | C2×D7 | semidirect |
| 66. C3×C7 | C2×M16 | semidirect |
| 70. M16 | D21 | direct (N × H) |
| 92. C8 | C2×D21 | semidirect |
| 93. C7 | D3×M16 | semidirect |
| 106. C3 | D7×M16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D21 | 2 |
| C3×C7×M16 | 2 |
| #66627 | 2 |
| #66622 | 2 |
| C8×D21 | 2 |
| D7×M16 | 3 |
| D3×M16 | 7 |