Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
384 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 168 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 |
|---|---|---|
| 3. #6452⋊C3 | C2 | semidirect |
| 5. #6433⋊C3 | C2 | semidirect |
| 6. #6432⋊C3 | C2 | semidirect |
| 7. C4×ΓL(1,𝔽8)⋊Q8 | C2 | semidirect |
| 8. #90209 | C3 | semidirect |
| 24. #6452 | C2×C3 | semidirect |
| 26. #6433 | C2×C3 | semidirect |
| 27. #6432 | C2×C3 | semidirect |
| 28. C4×Dic14 | C2×C3 | semidirect |
| 119. ΓL(1,𝔽8) | #541 | semidirect |
| 154. C7 | C3×#541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| ΓL(1,𝔽8)×#117 | 2 |
| #6487⋊C3 | 2 |
| #6452⋊C3 | 2 |
| #6442⋊C3 | 2 |
| #6433⋊C3 | 2 |
| #6432⋊C3 | 2 |
| C4×ΓL(1,𝔽8)⋊Q8 | 2 |
| #90209 | 3 |
| C3×#541 | 7 |