Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
208 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 68 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. C3×#6511 | C2 | semidirect |
| 3. #10620852 | C2 | semidirect |
| 4. C7×#837 | C2 | semidirect |
| 5. #10620527 | C2 | semidirect |
| 6. #10620515 | C2 | semidirect |
| 7. #10620488 | C2 | semidirect |
| 11. #66635 | C4 | semidirect |
| 12. #66634 | C4 | semidirect |
| 13. #66633 | C4 | semidirect |
| 14. #66632 | C4 | semidirect |
| 25. #6511 | D3 | semidirect |
| 66. #837 | D7 | semidirect |
| 145. C3×C7 | #444 | semidirect |
| 189. C7 | #5145 | semidirect |
| 202. C3 | #89595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621433 | 2 |
| C3×#6511 | 2 |
| #10620852 | 2 |
| C7×#837 | 2 |
| #10620527 | 2 |
| #10620515 | 2 |
| #10620488 | 2 |
| #89595 | 3 |
| #5145 | 7 |