Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
240 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 2. Q8×ΓL(1,𝔽8)⋊C4 | C2 | semidirect |
| 4. #6409⋊C3 | C2 | semidirect |
| 6. #6392⋊C3 | C2 | semidirect |
| 7. #6389⋊C3 | C2 | semidirect |
| 8. #89936 | C3 | semidirect |
| 12. SD16×ΓL(1,𝔽8) | C4 | semidirect |
| 22. Q8×Dic7 | C2×C3 | semidirect |
| 24. #6409 | C2×C3 | semidirect |
| 26. #6392 | C2×C3 | semidirect |
| 27. #6389 | C2×C3 | semidirect |
| 31. Q8×ΓL(1,𝔽8) | C2×C4 | semidirect |
| 41. C8×ΓL(1,𝔽8) | C2×C4 | semidirect |
| 46. C7×SD16 | C3×C4 | semidirect |
| 76. C7×Q8 | C2×C3×C4 | semidirect |
| 86. C7×C8 | C2×C3×C4 | semidirect |
| 136. ΓL(1,𝔽8) | #440 | semidirect |
| 140. SD16 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 166. Q8 | C2×ΓL(1,𝔽8)⋊C4 | semidirect |
| 177. C8 | C2×ΓL(1,𝔽8)⋊C4 | 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 |
|---|---|
| C2×SD16×ΓL(1,𝔽8) | 2 |
| Q8×ΓL(1,𝔽8)⋊C4 | 2 |
| D4×ΓL(1,𝔽8)⋊C4 | 2 |
| #6409⋊C3 | 2 |
| #6406⋊C3 | 2 |
| #6392⋊C3 | 2 |
| #6389⋊C3 | 2 |
| #89936 | 3 |
| C3×#440 | 7 |