Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
496 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 126 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. #10621577 | C2 | semidirect |
| 2. Q16×D21 | C2 | semidirect |
| 3. C7×#919 | C2 | semidirect |
| 4. C3×D7×Q16 | C2 | semidirect |
| 5. #10621086 | C2 | semidirect |
| 6. #10621075 | C2 | semidirect |
| 7. #10621072 | C2 | semidirect |
| 8. #10620841 | C2 | semidirect |
| 9. #10620832 | C2 | semidirect |
| 10. #10620827 | C2 | semidirect |
| 11. D3×Dic28 | C2 | semidirect |
| 44. D7×Q16 | D3 | semidirect |
| 110. #919 | D7 | semidirect |
| 237. C3×C7 | #578 | semidirect |
| 308. C7 | #5766 | semidirect |
| 325. C3 | #90462 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621577 | 2 |
| Q16×D21 | 2 |
| C7×#919 | 2 |
| C3×D7×Q16 | 2 |
| #10621086 | 2 |
| #10621075 | 2 |
| #10621072 | 2 |
| #10620841 | 2 |
| #10620832 | 2 |
| #10620827 | 2 |
| D3×Dic28 | 2 |
| #90462 | 3 |
| #5766 | 7 |