Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
124 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 124 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. #66732 | C2 | semidirect |
| 2. #66672 | C2 | semidirect |
| 3. C7×#215 | C2 | semidirect |
| 4. C3×#1144 | C2 | semidirect |
| 5. #66566 | C2 | semidirect |
| 6. #66562 | C2 | semidirect |
| 7. D21⋊C8 | C2 | semidirect |
| 23. #1144 | D3 | semidirect |
| 50. #215 | D7 | semidirect |
| 76. C3×C7 | #135 | semidirect |
| 106. C7 | #919 | semidirect |
| 118. C3 | #6479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66732 | 2 |
| #66672 | 2 |
| C7×#215 | 2 |
| C3×#1144 | 2 |
| #66566 | 2 |
| #66562 | 2 |
| D21⋊C8 | 2 |
| #6479 | 3 |
| #919 | 7 |