Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
212 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 212 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 |
|---|---|---|
| 1. ΓL(1,𝔽8)×#117 | C2 | semidirect |
| 3. (C22⋊(C7⋊C8))⋊C3 | C2 | semidirect |
| 4. #6383⋊C3 | C2 | semidirect |
| 5. #6383⋊C3 | C2 | semidirect |
| 6. #6382⋊C3 | C2 | semidirect |
| 7. #6381⋊C3 | C2 | semidirect |
| 8. #89775 | C3 | semidirect |
| 20. C7×#117 | C2×C3 | semidirect |
| 22. C22⋊(C7⋊C8) | C2×C3 | semidirect |
| 23. #6383 | C2×C3 | semidirect |
| 24. #6383 | C2×C3 | semidirect |
| 25. #6382 | C2×C3 | semidirect |
| 26. #6381 | C2×C3 | semidirect |
| 105. #117 | AGL(1,𝔽7) | semidirect |
| 138. ΓL(1,𝔽8) | #482 | semidirect |
| 182. C7 | C3×#482 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| ΓL(1,𝔽8)×#117 | 2 |
| #6493⋊C3 | 2 |
| (C22⋊(C7⋊C8))⋊C3 | 2 |
| #6383⋊C3 | 2 |
| #6382⋊C3 | 2 |
| #6381⋊C3 | 2 |
| #89775 | 3 |
| C3×#482 | 7 |