Finite Group DatabasebetaFinite Group DatabasebetaOrder 672.
124 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 40 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×#1161 | C2 | semidirect |
| 2. #66677 | C2 | semidirect |
| 3. #66634 | C2 | semidirect |
| 4. C7×#216 | C2 | semidirect |
| 5. #66563 | C2 | semidirect |
| 6. #66561 | C2 | semidirect |
| 7. D7×C3⋊C8 | C2 | semidirect |
| 21. #1161 | D3 | semidirect |
| 48. #216 | D7 | semidirect |
| 76. C3×C7 | #135 | semidirect |
| 106. C7 | #950 | semidirect |
| 118. C3 | #6482 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#1161 | 2 |
| #66677 | 2 |
| #66634 | 2 |
| C7×#216 | 2 |
| #66563 | 2 |
| #66561 | 2 |
| D7×C3⋊C8 | 2 |
| #6482 | 3 |
| #950 | 7 |