Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
240 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 62 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. #10620945 | C2 | semidirect |
| 3. C2×#66568 | C2 | semidirect |
| 4. C2×#66559 | C2 | semidirect |
| 5. C7×#810 | C2 | semidirect |
| 6. C3×#6381 | C2 | semidirect |
| 7. #10620503 | C2 | semidirect |
| 28. #6381 | D3 | semidirect |
| 44. C3×C7⋊C8 | D4 | semidirect |
| 64. #810 | D7 | semidirect |
| 95. C7⋊C8 | D12 | semidirect |
| 150. C3×C7 | #468 | semidirect |
| 198. C7 | #4886 | semidirect |
| 217. C3 | #89584 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621378 | 2 |
| #10620945 | 2 |
| C2×#66568 | 2 |
| C2×#66559 | 2 |
| C7×#810 | 2 |
| C3×#6381 | 2 |
| #10620503 | 2 |
| #89584 | 3 |
| #4886 | 7 |