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 |
|---|---|---|
| 2. C4×Q8×ΓL(1,𝔽8) | C2 | semidirect |
| 3. Q8×ΓL(1,𝔽8)⋊C4 | C2 | semidirect |
| 5. #6450⋊C3 | C2 | semidirect |
| 7. C4×ΓL(1,𝔽8)⋊Q8 | C2 | semidirect |
| 8. #90263 | C3 | semidirect |
| 10. Q8×AGL(1,𝔽7) | C4 | semidirect |
| 23. C4×C7×Q8 | C2×C3 | semidirect |
| 24. Q8×Dic7 | C2×C3 | semidirect |
| 26. #6450 | C2×C3 | semidirect |
| 28. C4×Dic14 | C2×C3 | semidirect |
| 41. Q8×D7 | C3×C4 | semidirect |
| 102. C4×Q8 | AGL(1,𝔽7) | semidirect |
| 125. ΓL(1,𝔽8) | #519 | semidirect |
| 163. C7 | C3×#519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×AGL(1,𝔽7) | 2 |
| C4×Q8×ΓL(1,𝔽8) | 2 |
| Q8×ΓL(1,𝔽8)⋊C4 | 2 |
| #6455⋊C3 | 2 |
| #6450⋊C3 | 2 |
| #6435⋊C3 | 2 |
| C4×ΓL(1,𝔽8)⋊Q8 | 2 |
| #90263 | 3 |
| C3×#519 | 7 |