Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
264 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 92 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. D4×ΓL(1,𝔽8)⋊C4 | C2 | semidirect |
| 3. #6406⋊C3 | C2 | semidirect |
| 4. #6391⋊C3 | C2 | semidirect |
| 5. #6389⋊C3 | C2 | semidirect |
| 6. #89924 | C3 | semidirect |
| 9. D8×ΓL(1,𝔽8) | C4 | semidirect |
| 16. D4×Dic7 | C2×C3 | semidirect |
| 17. #6406 | C2×C3 | semidirect |
| 18. #6391 | C2×C3 | semidirect |
| 19. #6389 | C2×C3 | semidirect |
| 23. D4×ΓL(1,𝔽8) | C2×C4 | semidirect |
| 28. C8×ΓL(1,𝔽8) | C2×C4 | semidirect |
| 32. C7×D8 | C3×C4 | semidirect |
| 54. C7×D4 | C2×C3×C4 | semidirect |
| 59. C7×C8 | C2×C3×C4 | semidirect |
| 94. ΓL(1,𝔽8) | #442 | semidirect |
| 97. D8 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 116. D4 | C2×ΓL(1,𝔽8)⋊C4 | semidirect |
| 122. C8 | C2×ΓL(1,𝔽8)⋊C4 | semidirect |
| 123. C7 | C3×#442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×ΓL(1,𝔽8) | 2 |
| D4×ΓL(1,𝔽8)⋊C4 | 2 |
| #6406⋊C3 | 2 |
| #6391⋊C3 | 2 |
| #6389⋊C3 | 2 |
| #89924 | 3 |
| C3×#442 | 7 |