Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
248 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 1. C4×D4×ΓL(1,𝔽8) | C2 | semidirect |
| 2. C2×#1142⋊C3 | C2 | semidirect |
| 4. #6438⋊C3 | C2 | semidirect |
| 5. #6384⋊C3 | C2 | semidirect |
| 6. #6383⋊C3 | C2 | semidirect |
| 7. C4⋊(ΓL(1,𝔽8)⋊C8) | C2 | semidirect |
| 8. #89788 | C3 | semidirect |
| 22. C4×C7×D4 | C2×C3 | semidirect |
| 23. C2×#1142 | C2×C3 | semidirect |
| 25. #6438 | C2×C3 | semidirect |
| 26. #6384 | C2×C3 | semidirect |
| 27. #6383 | C2×C3 | semidirect |
| 28. C4⋊(C7⋊C8) | C2×C3 | semidirect |
| 117. C4×D4 | AGL(1,𝔽7) | semidirect |
| 150. ΓL(1,𝔽8) | #463 | semidirect |
| 198. C7 | C3×#463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×ΓL(1,𝔽8) | 2 |
| C2×#1142⋊C3 | 2 |
| C2×#1141⋊C3 | 2 |
| #6438⋊C3 | 2 |
| #6384⋊C3 | 2 |
| #6383⋊C3 | 2 |
| C4⋊(ΓL(1,𝔽8)⋊C8) | 2 |
| #89788 | 3 |
| C3×#463 | 7 |