Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
220 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 3. C2×#66571 | C2 | semidirect |
| 5. #10620649 | C2 | semidirect |
| 6. C3×#6382 | C2 | semidirect |
| 7. #10620507 | C2 | semidirect |
| 28. #6382 | D3 | semidirect |
| 142. C3×C7 | #470 | semidirect |
| 186. C7 | #4867 | semidirect |
| 202. C3 | #89824 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#897 | 2 |
| #10620927 | 2 |
| C2×#66571 | 2 |
| C2×#66558 | 2 |
| #10620649 | 2 |
| C3×#6382 | 2 |
| #10620507 | 2 |
| #89824 | 3 |
| #4867 | 7 |