Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
304 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 304 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 |
|---|---|---|
| 2. C2×Q16×ΓL(1,𝔽8) | C2 | semidirect |
| 3. #6509⋊C3 | C2 | semidirect |
| 4. C2×#1143⋊C3 | C2 | semidirect |
| 5. #6409⋊C3 | C2 | semidirect |
| 6. #6395⋊C3 | C2 | semidirect |
| 7. (C2×AGL(1,𝔽7))⋊C8 | C2 | semidirect |
| 8. #89959 | C3 | semidirect |
| 25. C2×C7×Q16 | C2×C3 | semidirect |
| 26. #6509 | C2×C3 | semidirect |
| 27. C2×#1143 | C2×C3 | semidirect |
| 28. #6409 | C2×C3 | semidirect |
| 29. #6395 | C2×C3 | semidirect |
| 30. (C2×D7)⋊C8 | C2×C3 | semidirect |
| 127. C2×Q16 | AGL(1,𝔽7) | semidirect |
| 165. ΓL(1,𝔽8) | #452 | semidirect |
| 218. C7 | C3×#452 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66659 | 2 |
| C2×Q16×ΓL(1,𝔽8) | 2 |
| #6509⋊C3 | 2 |
| C2×#1143⋊C3 | 2 |
| #6409⋊C3 | 2 |
| #6395⋊C3 | 2 |
| (C2×AGL(1,𝔽7))⋊C8 | 2 |
| #89959 | 3 |
| C3×#452 | 7 |