Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
208 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 54 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. #10620883 | C2 | semidirect |
| 3. C2×#66568 | C2 | semidirect |
| 4. #10620852 | C2 | semidirect |
| 5. C7×#824 | C2 | semidirect |
| 6. C3×#6396 | C2 | semidirect |
| 7. #10620495 | C2 | semidirect |
| 30. #6396 | D3 | semidirect |
| 68. #824 | D7 | semidirect |
| 145. C3×C7 | #471 | semidirect |
| 189. C7 | #4898 | semidirect |
| 202. C3 | #89526 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621391 | 2 |
| #10620883 | 2 |
| C2×#66568 | 2 |
| #10620852 | 2 |
| C7×#824 | 2 |
| C3×#6396 | 2 |
| #10620495 | 2 |
| #89526 | 3 |
| #4898 | 7 |