Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
660 conjugacy classes of subgroups; only the 296 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 296 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. C2×C4⋊C4×ΓL(1,𝔽8) | C2 | semidirect |
| 4. C2×C4⋊(ΓL(1,𝔽8)⋊C4) | C2 | semidirect |
| 5. C2×C4×ΓL(1,𝔽8)⋊C4 | C2 | semidirect |
| 6. #6455⋊C3 | C2 | direct (N × H) |
| 7. C2×#6455 | C3 | semidirect |
| 13. C2×C4×AGL(1,𝔽7) | C4 | semidirect |
| 15. C4⋊C4×ΓL(1,𝔽8) | C22 | semidirect |
| 17. C4⋊(ΓL(1,𝔽8)⋊C4) | C22 | semidirect |
| 18. C4×ΓL(1,𝔽8)⋊C4 | C22 | semidirect |
| 20. C2×C7×C4⋊C4 | C2×C3 | semidirect |
| 22. C2×C4⋊Dic7 | C2×C3 | semidirect |
| 23. C2×C4×Dic7 | C2×C3 | semidirect |
| 24. #6455 | C2×C3 | semidirect |
| 39. C4×AGL(1,𝔽7) | C2×C4 | semidirect |
| 45. C2×C4×D7 | C3×C4 | semidirect |
| 47. C7×C4⋊C4 | C22×C3 | semidirect |
| 49. C4⋊Dic7 | C22×C3 | semidirect |
| 50. C4×Dic7 | C22×C3 | semidirect |
| 83. C4×D7 | C2×C3×C4 | semidirect |
| 95. C2×ΓL(1,𝔽8) | #117 | semidirect |
| 103. C2×C4⋊C4 | AGL(1,𝔽7) | semidirect |
| 132. ΓL(1,𝔽8) | C2×#117 | semidirect |
| 141. C4⋊C4 | C2×AGL(1,𝔽7) | semidirect |
| 144. C2×C7 | C3×#117 | semidirect |
| 175. C7 | C2×C3×#117 | semidirect |
| 195. C2 | #6455⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×AGL(1,𝔽7) | 2 |
| C2×C4⋊C4×ΓL(1,𝔽8) | 2 |
| C2×(C2×AGL(1,𝔽7))⋊C4 | 2 |
| C2×C4⋊(ΓL(1,𝔽8)⋊C4) | 2 |
| C2×C4×ΓL(1,𝔽8)⋊C4 | 2 |
| #6455⋊C3 | 2 |
| C2×#6455 | 3 |
| C2×C3×#117 | 7 |