Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
444 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 192 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)×#125 | C2 | semidirect |
| 4. #6451⋊C3 | C2 | semidirect |
| 5. #6450⋊C3 | C2 | semidirect |
| 7. #6433⋊C3 | C2 | semidirect |
| 8. #90379 | C3 | semidirect |
| 22. C7×#125 | C2×C3 | semidirect |
| 25. #6451 | C2×C3 | semidirect |
| 26. #6450 | C2×C3 | semidirect |
| 28. #6433 | C2×C3 | semidirect |
| 38. C4×AGL(1,𝔽7) | Q8 | semidirect |
| 78. C4×D7 | C3×Q8 | semidirect |
| 98. #125 | AGL(1,𝔽7) | semidirect |
| 122. ΓL(1,𝔽8) | #533 | semidirect |
| 158. C7 | C3×#533 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| ΓL(1,𝔽8)×#125 | 2 |
| #6459⋊C3 | 2 |
| #6455⋊C3 | 2 |
| #6451⋊C3 | 2 |
| #6450⋊C3 | 2 |
| C42×AGL(1,𝔽7) | 2 |
| #6433⋊C3 | 2 |
| #90379 | 3 |
| C3×#533 | 7 |