Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
188 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 88 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. #89600 | C3 | semidirect |
| 39. ΓL(1,𝔽8)⋊C8 | Q8 | semidirect |
| 79. C7⋊C8 | C3×Q8 | semidirect |
| 122. ΓL(1,𝔽8) | #446 | semidirect |
| 158. C7 | C3×#446 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×ΓL(1,𝔽8)⋊Q8 | 2 |
| ΓL(1,𝔽8)×C4⋊C8 | 2 |
| #6389⋊C3 | 2 |
| (ΓL(1,𝔽8)⋊C4)⋊C8 | 2 |
| C8×ΓL(1,𝔽8)⋊C4 | 2 |
| #6377⋊C3 | 2 |
| #89600 | 3 |
| C3×#446 | 7 |