Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
292 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 66 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. #10621519 | C2 | semidirect |
| 2. ΓL(1,𝔽8)×AGL(1,ℤ/8) | C2 | semidirect |
| 3. #6499⋊C3 | C2 | semidirect |
| 4. #6495⋊C3 | C2 | semidirect |
| 5. #6411⋊C3 | C2 | semidirect |
| 6. #6399⋊C3 | C2 | semidirect |
| 7. #6398⋊C3 | C2 | semidirect |
| 8. #89973 | C3 | semidirect |
| 26. #6554 | C2×C3 | semidirect |
| 27. C7×AGL(1,ℤ/8) | C2×C3 | semidirect |
| 28. #6499 | C2×C3 | semidirect |
| 29. #6495 | C2×C3 | semidirect |
| 30. #6411 | C2×C3 | semidirect |
| 31. #6399 | C2×C3 | semidirect |
| 32. #6398 | C2×C3 | semidirect |
| 138. AGL(1,ℤ/8) | AGL(1,𝔽7) | semidirect |
| 176. ΓL(1,𝔽8) | #454 | semidirect |
| 232. C7 | C3×#454 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621519 | 2 |
| ΓL(1,𝔽8)×AGL(1,ℤ/8) | 2 |
| #6499⋊C3 | 2 |
| #6495⋊C3 | 2 |
| #6411⋊C3 | 2 |
| #6399⋊C3 | 2 |
| #6398⋊C3 | 2 |
| #89973 | 3 |
| C3×#454 | 7 |