Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
124 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 47 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×C7×#41 | C2 | semidirect |
| 2. #66728 | C2 | semidirect |
| 3. #66635 | C2 | semidirect |
| 4. #66634 | C2 | semidirect |
| 5. #66633 | C2 | semidirect |
| 6. #66632 | C2 | semidirect |
| 7. C2×C3⋊(C7⋊C8) | C2 | semidirect |
| 20. C7×#41 | D3 | semidirect |
| 46. C3×#41 | D7 | semidirect |
| 76. C3×C7 | #135 | semidirect |
| 78. #41 | D21 | semidirect |
| 106. C7 | #950 | semidirect |
| 118. C3 | #6513 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×#41 | 2 |
| #66728 | 2 |
| #66635 | 2 |
| #66634 | 2 |
| #66633 | 2 |
| #66632 | 2 |
| C2×C3⋊(C7⋊C8) | 2 |
| #6513 | 3 |
| #950 | 7 |