Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
468 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 134 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. #10621380 | C2 | semidirect |
| 2. C7×#893 | C2 | semidirect |
| 3. C3×#6453 | C2 | semidirect |
| 5. #10621008 | C2 | semidirect |
| 6. #10621000 | C2 | semidirect |
| 7. C4×D21⋊C4 | C2 | semidirect |
| 8. #10620935 | C2 | semidirect |
| 9. #10620904 | C2 | semidirect |
| 10. #10620902 | C2 | semidirect |
| 11. #10620900 | C2 | semidirect |
| 42. #6453 | D3 | semidirect |
| 95. #893 | D7 | semidirect |
| 208. C3×C7 | #529 | semidirect |
| 271. C7 | #5691 | semidirect |
| 293. C3 | #90248 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621380 | 2 |
| C7×#893 | 2 |
| C3×#6453 | 2 |
| #10621028 | 2 |
| #10621008 | 2 |
| #10621000 | 2 |
| C4×D21⋊C4 | 2 |
| #10620935 | 2 |
| #10620904 | 2 |
| #10620902 | 2 |
| #10620900 | 2 |
| #90248 | 3 |
| #5691 | 7 |