Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
410 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 73 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. Dic14⋊A4 | C2 | direct (N × H) |
| 4. C23×Dic14 | C3 | semidirect |
| 15. C22×Dic14 | C2×C3 | semidirect |
| 17. C2×C22⋊ΓL(1,𝔽8) | Q8 | semidirect |
| 40. C2×Dic14 | A4 | semidirect |
| 44. C22⋊ΓL(1,𝔽8) | C2×Q8 | semidirect |
| 52. C23×C7 | C3×Q8 | semidirect |
| 69. Dic14 | C2×A4 | semidirect |
| 90. C22×C7 | C2×C3×Q8 | semidirect |
| 124. C2×C7 | Q8×A4 | semidirect |
| 133. C23 | ΓL(1,𝔽8)⋊Q8 | semidirect |
| 151. C7 | C2×Q8×A4 | semidirect |
| 161. C22 | C2×ΓL(1,𝔽8)⋊Q8 | semidirect |
| 171. C2 | Dic14⋊A4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊ΓL(1,𝔽8) | 2 |
| C2×Dic7⋊A4 | 2 |
| Dic14⋊A4 | 2 |
| C23×Dic14 | 3 |
| C2×ΓL(1,𝔽8)⋊Q8 | 4 |
| C2×Q8×A4 | 7 |