Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
240 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 3. C4×ΓL(1,𝔽8)⋊Q8 | C2 | semidirect |
| 5. #6384⋊C3 | C2 | semidirect |
| 6. #6381⋊C3 | C2 | semidirect |
| 7. #6377⋊C3 | C2 | semidirect |
| 8. #89790 | C3 | semidirect |
| 15. #1142⋊C3 | C4 | semidirect |
| 23. C4×Dic14 | C2×C3 | semidirect |
| 25. #6384 | C2×C3 | semidirect |
| 26. #6381 | C2×C3 | semidirect |
| 27. #6377 | C2×C3 | semidirect |
| 40. ΓL(1,𝔽8)⋊Q8 | C2×C4 | semidirect |
| 42. ΓL(1,𝔽8)⋊C8 | C2×C4 | semidirect |
| 49. #1142 | C3×C4 | semidirect |
| 85. Dic14 | C2×C3×C4 | semidirect |
| 87. C7⋊C8 | C2×C3×C4 | semidirect |
| 136. ΓL(1,𝔽8) | #440 | semidirect |
| 178. C7 | C3×#440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×ΓL(1,𝔽8) | 2 |
| C2×#1142⋊C3 | 2 |
| C4×ΓL(1,𝔽8)⋊Q8 | 2 |
| #6406⋊C3 | 2 |
| #6384⋊C3 | 2 |
| #6381⋊C3 | 2 |
| #6377⋊C3 | 2 |
| #89790 | 3 |
| C3×#440 | 7 |