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 |
|---|---|---|
| 1. ΓL(1,𝔽8)×#137 | C2 | semidirect |
| 3. #10620784 | C2 | semidirect |
| 4. C2×#1143⋊C3 | C2 | semidirect |
| 5. #6410⋊C3 | C2 | semidirect |
| 6. #6397⋊C3 | C2 | semidirect |
| 7. #6396⋊C3 | C2 | semidirect |
| 8. #89975 | C3 | semidirect |
| 24. C7×#137 | C2×C3 | semidirect |
| 26. #6511 | C2×C3 | semidirect |
| 27. C2×#1143 | C2×C3 | semidirect |
| 28. #6410 | C2×C3 | semidirect |
| 29. #6397 | C2×C3 | semidirect |
| 30. #6396 | C2×C3 | semidirect |
| 114. #137 | AGL(1,𝔽7) | 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)×#137 | 2 |
| #6512⋊C3 | 2 |
| #10620784 | 2 |
| C2×#1143⋊C3 | 2 |
| #6410⋊C3 | 2 |
| #6397⋊C3 | 2 |
| #6396⋊C3 | 2 |
| #89975 | 3 |
| C3×#471 | 7 |