Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
472 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 174 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. #6499⋊C3 | C2 | semidirect |
| 3. #6498⋊C3 | C2 | semidirect |
| 4. D4×ΓL(1,𝔽8)⋊C4 | C2 | semidirect |
| 5. C4×ΓL(1,𝔽8)⋊Q8 | C2 | semidirect |
| 6. #90404 | C3 | semidirect |
| 18. #6499 | C2×C3 | semidirect |
| 19. #6498 | C2×C3 | semidirect |
| 20. D4×Dic7 | C2×C3 | semidirect |
| 21. C4×Dic14 | C2×C3 | semidirect |
| 98. ΓL(1,𝔽8) | #559 | semidirect |
| 128. C7 | C3×#559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| ΓL(1,𝔽8)×#127 | 2 |
| #6499⋊C3 | 2 |
| #6498⋊C3 | 2 |
| D4×ΓL(1,𝔽8)⋊C4 | 2 |
| C4×ΓL(1,𝔽8)⋊Q8 | 2 |
| #90404 | 3 |
| C3×#559 | 7 |