Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
216 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 72 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. #89954 | C3 | semidirect |
| 73. ΓL(1,𝔽8)⋊C4 | Q16 | semidirect |
| 121. Dic7 | C3×Q16 | semidirect |
| 137. ΓL(1,𝔽8) | #462 | semidirect |
| 178. C7 | C3×#462 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×ΓL(1,𝔽8) | 2 |
| Q8×ΓL(1,𝔽8)⋊C4 | 2 |
| #6507⋊C3 | 2 |
| C2×#1144⋊C3 | 2 |
| #6409⋊C3 | 2 |
| #6390⋊C3 | 2 |
| (ΓL(1,𝔽8)⋊C4)⋊C8 | 2 |
| #89954 | 3 |
| C3×#462 | 7 |