Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
304 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 72 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×#6487 | C2 | semidirect |
| 3. C2×#66569 | C2 | semidirect |
| 4. C2×#66564 | C2 | semidirect |
| 5. #10620669 | C2 | semidirect |
| 6. #10620507 | C2 | semidirect |
| 7. #10620501 | C2 | semidirect |
| 27. #6487 | D3 | semidirect |
| 165. C3×C7 | #452 | semidirect |
| 218. C7 | #5047 | semidirect |
| 237. C3 | #90011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#235 | 2 |
| C3×#6487 | 2 |
| C2×#66569 | 2 |
| C2×#66564 | 2 |
| #10620669 | 2 |
| #10620507 | 2 |
| #10620501 | 2 |
| #90011 | 3 |
| #5047 | 7 |