Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
208 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 208 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. #6514⋊C3 | C2 | semidirect |
| 3. #10620784 | C2 | semidirect |
| 4. C2×#1142⋊C3 | C2 | semidirect |
| 5. #6407⋊C3 | C2 | semidirect |
| 6. #6398⋊C3 | C2 | semidirect |
| 7. #6396⋊C3 | C2 | semidirect |
| 8. #89972 | C3 | semidirect |
| 25. #6514 | C2×C3 | semidirect |
| 26. #6511 | C2×C3 | semidirect |
| 27. C2×#1142 | C2×C3 | semidirect |
| 28. #6407 | C2×C3 | semidirect |
| 29. #6398 | C2×C3 | semidirect |
| 30. #6396 | C2×C3 | semidirect |
| 145. ΓL(1,𝔽8) | #471 | semidirect |
| 189. C7 | C3×#471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| ΓL(1,𝔽8)×AGL(1,ℤ/8) | 2 |
| #6514⋊C3 | 2 |
| #10620784 | 2 |
| C2×#1142⋊C3 | 2 |
| #6407⋊C3 | 2 |
| #6398⋊C3 | 2 |
| #6396⋊C3 | 2 |
| #89972 | 3 |
| C3×#471 | 7 |