Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
532 conjugacy classes of subgroups; only the 272 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 272 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 |
|---|---|---|
| 4. #6450⋊C3 | C2 | semidirect |
| 6. C4×ΓL(1,𝔽8)⋊Q8 | C2 | semidirect |
| 7. #90207 | C3 | semidirect |
| 10. C2×ΓL(1,𝔽8)⋊Q8 | C4 | semidirect |
| 24. #6450 | C2×C3 | semidirect |
| 26. C4×Dic14 | C2×C3 | semidirect |
| 40. C2×Dic14 | C3×C4 | semidirect |
| 116. ΓL(1,𝔽8) | #519 | semidirect |
| 151. C7 | C3×#519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×ΓL(1,𝔽8)⋊Q8 | 2 |
| ΓL(1,𝔽8)×#117 | 2 |
| #6489⋊C3 | 2 |
| #6450⋊C3 | 2 |
| #6440⋊C3 | 2 |
| C4×ΓL(1,𝔽8)⋊Q8 | 2 |
| #90207 | 3 |
| C3×#519 | 7 |