Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
324 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 324 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 |
|---|---|---|
| 1. C2×#66728 | C2 | semidirect |
| 2. C7×#930 | C2 | semidirect |
| 3. C2×#66567 | C2 | semidirect |
| 4. C2×#66562 | C2 | semidirect |
| 5. C3×C22⋊(C7⋊C8) | C2 | semidirect |
| 6. #10620510 | C2 | semidirect |
| 7. #10620504 | C2 | semidirect |
| 28. C22⋊(C7⋊C8) | D3 | semidirect |
| 42. D84 | D4 | semidirect |
| 45. Dic42 | D4 | semidirect |
| 68. #930 | D7 | semidirect |
| 173. C3×C7 | #449 | semidirect |
| 230. C7 | #4734 | semidirect |
| 252. C3 | #89809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66728 | 2 |
| C7×#930 | 2 |
| C2×#66567 | 2 |
| C2×#66562 | 2 |
| C3×C22⋊(C7⋊C8) | 2 |
| #10620510 | 2 |
| #10620504 | 2 |
| #89809 | 3 |
| #4734 | 7 |