Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
224 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 68 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×Dic28⋊C3 | C2 | semidirect |
| 4. C4×ΓL(1,𝔽8)⋊Q8 | C2 | semidirect |
| 5. ΓL(1,𝔽8)×C4⋊C8 | C2 | semidirect |
| 7. #6390⋊C3 | C2 | semidirect |
| 8. #89617 | C3 | semidirect |
| 22. C2×Dic28 | C2×C3 | semidirect |
| 25. C4×Dic14 | C2×C3 | semidirect |
| 26. C7×C4⋊C8 | C2×C3 | semidirect |
| 28. #6390 | C2×C3 | semidirect |
| 113. C4⋊C8 | AGL(1,𝔽7) | semidirect |
| 142. ΓL(1,𝔽8) | #464 | semidirect |
| 186. C7 | C3×#464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic28⋊C3 | 2 |
| C2×#1132⋊C3 | 2 |
| #6438⋊C3 | 2 |
| C4×ΓL(1,𝔽8)⋊Q8 | 2 |
| ΓL(1,𝔽8)×C4⋊C8 | 2 |
| #6395⋊C3 | 2 |
| #6390⋊C3 | 2 |
| #89617 | 3 |
| C3×#464 | 7 |