Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
540 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 160 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. C22×C7×Dic6 | C2 | semidirect |
| 3. C3×#6489 | C2 | semidirect |
| 4. #10621104 | C2 | semidirect |
| 5. #10620945 | C2 | semidirect |
| 6. #10620938 | C2 | semidirect |
| 7. #10620937 | C2 | semidirect |
| 30. #6489 | D3 | semidirect |
| 63. C22×Dic6 | D7 | semidirect |
| 146. C3×C7 | #536 | semidirect |
| 191. C7 | #5526 | semidirect |
| 206. C3 | #90507 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66728 | 2 |
| C22×C7×Dic6 | 2 |
| C3×#6489 | 2 |
| #10621104 | 2 |
| #10620945 | 2 |
| #10620938 | 2 |
| #10620937 | 2 |
| #90507 | 3 |
| #5526 | 7 |