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. #6487⋊C3 | C2 | semidirect |
| 3. C2×Dic28⋊C3 | C2 | semidirect |
| 4. C2×#1132⋊C3 | C2 | semidirect |
| 5. ΓL(1,𝔽8)×C22⋊C8 | C2 | semidirect |
| 6. #6395⋊C3 | C2 | semidirect |
| 7. #6390⋊C3 | C2 | semidirect |
| 8. #89505 | C3 | semidirect |
| 25. #6487 | C2×C3 | semidirect |
| 26. C2×Dic28 | C2×C3 | semidirect |
| 27. C2×#1132 | C2×C3 | semidirect |
| 28. C7×C22⋊C8 | C2×C3 | semidirect |
| 29. #6395 | C2×C3 | semidirect |
| 30. #6390 | C2×C3 | semidirect |
| 132. C22⋊C8 | 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×#1157⋊C3 | 2 |
| #6487⋊C3 | 2 |
| C2×Dic28⋊C3 | 2 |
| C2×#1132⋊C3 | 2 |
| ΓL(1,𝔽8)×C22⋊C8 | 2 |
| #6395⋊C3 | 2 |
| #6390⋊C3 | 2 |
| #89505 | 3 |
| C3×#452 | 7 |