Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
192 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 8. #89626 | C3 | semidirect |
| 37. ΓL(1,𝔽8)⋊Q8 | Q8 | semidirect |
| 77. Dic14 | C3×Q8 | semidirect |
| 122. ΓL(1,𝔽8) | #475 | semidirect |
| 158. C7 | C3×#475 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #6451⋊C3 | 2 |
| #6450⋊C3 | 2 |
| ΓL(1,𝔽8)×#106 | 2 |
| #6390⋊C3 | 2 |
| (ΓL(1,𝔽8)⋊C4)⋊C8 | 2 |
| #6384⋊C3 | 2 |
| #6382⋊C3 | 2 |
| #89626 | 3 |
| C3×#475 | 7 |