Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
308 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 98 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. ΓL(1,𝔽8)×#117 | C2 | semidirect |
| 3. C2×#1136⋊C3 | C2 | semidirect |
| 4. #6379⋊C3 | C2 | semidirect |
| 5. #89777 | C3 | semidirect |
| 10. #1157⋊C3 | C4 | semidirect |
| 12. C2×C4⋊AGL(1,𝔽7) | C4 | semidirect |
| 14. C2×ΓL(1,𝔽8)⋊Q8 | C4 | semidirect |
| 17. C42×ΓL(1,𝔽8) | C22 | semidirect |
| 19. #1136⋊C3 | C22 | semidirect |
| 22. C7×#117 | C2×C3 | semidirect |
| 23. C2×#1136 | C2×C3 | semidirect |
| 24. #6379 | C2×C3 | semidirect |
| 49. #1157 | C3×C4 | semidirect |
| 51. C2×D28 | C3×C4 | semidirect |
| 53. C2×Dic14 | C3×C4 | semidirect |
| 56. C42×C7 | C22×C3 | semidirect |
| 58. #1136 | C22×C3 | semidirect |
| 118. #117 | AGL(1,𝔽7) | semidirect |
| 151. ΓL(1,𝔽8) | #421 | semidirect |
| 166. C42 | C2×AGL(1,𝔽7) | semidirect |
| 203. C7 | C3×#421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1157⋊C3 | 2 |
| ΓL(1,𝔽8)×#117 | 2 |
| C2×#1136⋊C3 | 2 |
| #6379⋊C3 | 2 |
| #89777 | 3 |
| C3×#421 | 7 |