Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
120 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 41 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. Q8×D21 | C2 | semidirect |
| 3. C3×C7×Q16 | C2 | semidirect |
| 4. #66635 | C2 | semidirect |
| 5. #66634 | C2 | semidirect |
| 6. #66623 | C2 | semidirect |
| 7. #66622 | C2 | semidirect |
| 22. C7×Q16 | D3 | semidirect |
| 48. C3×Q16 | D7 | semidirect |
| 75. C3×C7 | #137 | semidirect |
| 79. Q16 | D21 | semidirect |
| 104. C7 | #918 | semidirect |
| 115. C3 | #6481 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66732 | 2 |
| Q8×D21 | 2 |
| C3×C7×Q16 | 2 |
| #66635 | 2 |
| #66634 | 2 |
| #66623 | 2 |
| #66622 | 2 |
| #6481 | 3 |
| #918 | 7 |