Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
304 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 304 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. C7×#924 | C2 | semidirect |
| 3. C2×#66571 | C2 | semidirect |
| 4. C2×#66568 | C2 | semidirect |
| 5. C3×C22⋊(C7⋊C8) | C2 | semidirect |
| 6. #10620510 | C2 | semidirect |
| 7. #10620504 | C2 | semidirect |
| 28. C22⋊(C7⋊C8) | D3 | semidirect |
| 67. #924 | D7 | semidirect |
| 165. C3×C7 | #452 | semidirect |
| 218. C7 | #4733 | semidirect |
| 237. C3 | #89819 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66728 | 2 |
| C7×#924 | 2 |
| C2×#66571 | 2 |
| C2×#66568 | 2 |
| C3×C22⋊(C7⋊C8) | 2 |
| #10620510 | 2 |
| #10620504 | 2 |
| #89819 | 3 |
| #4733 | 7 |