Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
240 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 64 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. #10620927 | C2 | semidirect |
| 3. C2×#66567 | C2 | semidirect |
| 4. C2×#66558 | C2 | semidirect |
| 5. #10620649 | C2 | semidirect |
| 6. C3×#6381 | C2 | semidirect |
| 7. #10620501 | C2 | semidirect |
| 28. #6381 | D3 | semidirect |
| 45. C3×C7⋊C8 | D4 | semidirect |
| 95. C7⋊C8 | D12 | semidirect |
| 150. C3×C7 | #468 | semidirect |
| 198. C7 | #4886 | semidirect |
| 217. C3 | #89814 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#895 | 2 |
| #10620927 | 2 |
| C2×#66567 | 2 |
| C2×#66558 | 2 |
| #10620649 | 2 |
| C3×#6381 | 2 |
| #10620501 | 2 |
| #89814 | 3 |
| #4886 | 7 |