Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
111 conjugacy classes of subgroups.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. Q8×AGL(1,𝔽8) | C3 | semidirect |
| 6. AΓL(1,𝔽8) | Q8 | direct (N × H) |
| 13. C23×Q8 | ΓL(1,𝔽8) | semidirect |
| 14. AGL(1,𝔽8) | C3×Q8 | semidirect |
| 45. C23 | Q8×ΓL(1,𝔽8) | semidirect |
| 48. Q8 | AΓL(1,𝔽8) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×AΓL(1,𝔽8) | 2 |
| Q8×AGL(1,𝔽8) | 3 |
| C2×Q8×A4 | 7 |
| Q8×ΓL(1,𝔽8) | 8 |