Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
216 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 216 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)×AGL(1,ℤ/8) | C2 | semidirect |
| 2. #6512⋊C3 | C2 | semidirect |
| 3. #10620784 | C2 | semidirect |
| 4. C2×#1141⋊C3 | C2 | semidirect |
| 5. #6407⋊C3 | C2 | semidirect |
| 6. #6397⋊C3 | C2 | semidirect |
| 7. #6396⋊C3 | C2 | semidirect |
| 8. #89971 | C3 | semidirect |
| 24. C7×AGL(1,ℤ/8) | C2×C3 | semidirect |
| 25. #6512 | C2×C3 | semidirect |
| 26. #6511 | C2×C3 | semidirect |
| 27. C2×#1141 | C2×C3 | semidirect |
| 28. #6407 | C2×C3 | semidirect |
| 29. #6397 | C2×C3 | semidirect |
| 30. #6396 | C2×C3 | semidirect |
| 117. AGL(1,ℤ/8) | AGL(1,𝔽7) | semidirect |
| 148. ΓL(1,𝔽8) | #472 | semidirect |
| 194. C7 | C3×#472 | 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 |
| #6512⋊C3 | 2 |
| #10620784 | 2 |
| C2×#1141⋊C3 | 2 |
| #6407⋊C3 | 2 |
| #6397⋊C3 | 2 |
| #6396⋊C3 | 2 |
| #89971 | 3 |
| C3×#472 | 7 |