Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
260 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 260 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 |
|---|---|---|
| 1. C2×SD16×ΓL(1,𝔽8) | C2 | semidirect |
| 2. #6510⋊C3 | C2 | semidirect |
| 3. C2×#1144⋊C3 | C2 | semidirect |
| 4. #6499⋊C3 | C2 | semidirect |
| 6. C2×#1132⋊C3 | C2 | semidirect |
| 7. C8×ΓL(1,𝔽8)⋊C4 | C2 | semidirect |
| 8. #89940 | C3 | semidirect |
| 22. C2×C7×SD16 | C2×C3 | semidirect |
| 23. #6510 | C2×C3 | semidirect |
| 24. C2×#1144 | C2×C3 | semidirect |
| 25. #6499 | C2×C3 | semidirect |
| 27. C2×#1132 | C2×C3 | semidirect |
| 28. C8×Dic7 | C2×C3 | semidirect |
| 112. C2×SD16 | AGL(1,𝔽7) | semidirect |
| 143. ΓL(1,𝔽8) | #495 | semidirect |
| 187. C7 | C3×#495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×SD16×ΓL(1,𝔽8) | 2 |
| #6510⋊C3 | 2 |
| C2×#1144⋊C3 | 2 |
| #6499⋊C3 | 2 |
| C2×#1141⋊C3 | 2 |
| C2×#1132⋊C3 | 2 |
| C8×ΓL(1,𝔽8)⋊C4 | 2 |
| #89940 | 3 |
| C3×#495 | 7 |