Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
180 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 66 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. #89629 | C3 | semidirect |
| 119. ΓL(1,𝔽8) | #479 | semidirect |
| 154. C7 | C3×#479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #6453⋊C3 | 2 |
| #6450⋊C3 | 2 |
| ΓL(1,𝔽8)×#106 | 2 |
| #6390⋊C3 | 2 |
| (ΓL(1,𝔽8)⋊C4)⋊C8 | 2 |
| #6384⋊C3 | 2 |
| #6381⋊C3 | 2 |
| #89629 | 3 |
| C3×#479 | 7 |