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×#890 | C2 | semidirect |
| 3. C3×#6456 | C2 | semidirect |
| 5. #10621006 | C2 | semidirect |
| 6. C4×D21⋊C4 | C2 | semidirect |
| 7. #10620926 | C2 | semidirect |
| 8. #10620924 | C2 | semidirect |
| 9. #10620920 | C2 | semidirect |
| 10. #10620918 | C2 | semidirect |
| 11. #10620895 | C2 | semidirect |
| 42. #6456 | D3 | semidirect |
| 95. #890 | D7 | semidirect |
| 208. C3×C7 | #529 | semidirect |
| 271. C7 | #5557 | semidirect |
| 293. C3 | #90382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621380 | 2 |
| C7×#890 | 2 |
| C3×#6456 | 2 |
| #10621027 | 2 |
| #10621006 | 2 |
| C4×D21⋊C4 | 2 |
| #10620926 | 2 |
| #10620924 | 2 |
| #10620920 | 2 |
| #10620918 | 2 |
| #10620895 | 2 |
| #90382 | 3 |
| #5557 | 7 |