Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
260 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 4. #6389⋊C3 | C2 | semidirect |
| 5. C8×ΓL(1,𝔽8)⋊C4 | C2 | semidirect |
| 6. #89894 | C3 | semidirect |
| 8. M16×ΓL(1,𝔽8) | C4 | semidirect |
| 13. C2×ΓL(1,𝔽8)⋊C8 | C4 | semidirect |
| 19. #6389 | C2×C3 | semidirect |
| 20. C8×Dic7 | C2×C3 | semidirect |
| 32. C7×M16 | C3×C4 | semidirect |
| 37. C2×C7⋊C8 | C3×C4 | semidirect |
| 95. ΓL(1,𝔽8) | #405 | semidirect |
| 97. M16 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 124. C7 | C3×#405 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×ΓL(1,𝔽8) | 2 |
| #6489⋊C3 | 2 |
| C22×ΓL(1,𝔽8)⋊C8 | 2 |
| #6389⋊C3 | 2 |
| C8×ΓL(1,𝔽8)⋊C4 | 2 |
| #89894 | 3 |
| C3×#405 | 7 |