Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
424 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 174 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. C4×Q8×ΓL(1,𝔽8) | C2 | semidirect |
| 2. #6509⋊C3 | C2 | semidirect |
| 3. #6461⋊C3 | C2 | semidirect |
| 4. #6455⋊C3 | C2 | semidirect |
| 7. #6432⋊C3 | C2 | semidirect |
| 8. C4×ΓL(1,𝔽8)⋊Q8 | C2 | semidirect |
| 9. #90275 | C3 | semidirect |
| 26. C4×C7×Q8 | C2×C3 | semidirect |
| 27. #6509 | C2×C3 | semidirect |
| 28. #6461 | C2×C3 | semidirect |
| 29. #6455 | C2×C3 | semidirect |
| 32. #6432 | C2×C3 | semidirect |
| 33. C4×Dic14 | C2×C3 | semidirect |
| 120. C4×Q8 | AGL(1,𝔽7) | semidirect |
| 146. ΓL(1,𝔽8) | #556 | semidirect |
| 190. C7 | C3×#556 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×ΓL(1,𝔽8) | 2 |
| #6509⋊C3 | 2 |
| #6461⋊C3 | 2 |
| #6455⋊C3 | 2 |
| #6438⋊C3 | 2 |
| C4×C4⋊AGL(1,𝔽7) | 2 |
| #6432⋊C3 | 2 |
| C4×ΓL(1,𝔽8)⋊Q8 | 2 |
| #90275 | 3 |
| C3×#556 | 7 |