Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
208 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 86 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. #10620784 | C2 | semidirect |
| 3. #6411⋊C3 | C2 | semidirect |
| 4. #6393⋊C3 | C2 | semidirect |
| 5. #6389⋊C3 | C2 | semidirect |
| 6. #89969 | C3 | semidirect |
| 8. Q16×ΓL(1,𝔽8) | C4 | semidirect |
| 9. SD16×ΓL(1,𝔽8) | C4 | semidirect |
| 10. D8×ΓL(1,𝔽8) | C4 | semidirect |
| 18. #6511 | C2×C3 | semidirect |
| 19. #6411 | C2×C3 | semidirect |
| 20. #6393 | C2×C3 | semidirect |
| 21. #6389 | C2×C3 | semidirect |
| 34. C7×Q16 | C3×C4 | semidirect |
| 35. C7×SD16 | C3×C4 | semidirect |
| 36. C7×D8 | C3×C4 | semidirect |
| 99. ΓL(1,𝔽8) | #444 | semidirect |
| 101. Q16 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 102. SD16 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 103. D8 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 129. C7 | C3×#444 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| ΓL(1,𝔽8)×#135 | 2 |
| #10620784 | 2 |
| #6411⋊C3 | 2 |
| #6393⋊C3 | 2 |
| #6389⋊C3 | 2 |
| #89969 | 3 |
| C3×#444 | 7 |