Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
256 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 66 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×#66633 | C2 | semidirect |
| 3. #10620902 | C2 | semidirect |
| 4. C2×#66567 | C2 | semidirect |
| 5. C3×#6406 | C2 | semidirect |
| 6. Dic3⋊(C7⋊C8) | C2 | semidirect |
| 7. #10620501 | C2 | semidirect |
| 27. #6406 | D3 | semidirect |
| 37. Dic42 | D4 | semidirect |
| 79. C7×Dic3 | SD16 | semidirect |
| 153. C3×C7 | #460 | semidirect |
| 184. Dic3 | #1142 | semidirect |
| 202. C7 | #4762 | semidirect |
| 221. C3 | #89847 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66633 | 2 |
| C7×#940 | 2 |
| #10620902 | 2 |
| C2×#66567 | 2 |
| C3×#6406 | 2 |
| Dic3⋊(C7⋊C8) | 2 |
| #10620501 | 2 |
| #89847 | 3 |
| #4762 | 7 |