Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
236 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 65 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. #10621371 | C2 | semidirect |
| 3. C3×C7×#102 | C2 | semidirect |
| 4. #10620671 | C2 | semidirect |
| 5. #10620660 | C2 | semidirect |
| 6. C8×Dic21 | C2 | semidirect |
| 7. #10620648 | C2 | semidirect |
| 22. C7×#102 | D3 | semidirect |
| 57. C3×#102 | D7 | semidirect |
| 113. #102 | D21 | semidirect |
| 144. C3×C7 | #486 | semidirect |
| 190. C7 | #4760 | semidirect |
| 209. C3 | #89532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621423 | 2 |
| #10621371 | 2 |
| C3×C7×#102 | 2 |
| #10620671 | 2 |
| #10620660 | 2 |
| C8×Dic21 | 2 |
| #10620648 | 2 |
| #89532 | 3 |
| #4760 | 7 |