Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
240 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 68 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. ΓL(1,𝔽8)×C22⋊Q8 | C2 | semidirect |
| 2. C2×#1143⋊C3 | C2 | semidirect |
| 4. C2×#1136⋊C3 | C2 | semidirect |
| 5. #6409⋊C3 | C2 | semidirect |
| 6. #6383⋊C3 | C2 | semidirect |
| 7. #6381⋊C3 | C2 | semidirect |
| 8. #89821 | C3 | semidirect |
| 22. C7×C22⋊Q8 | C2×C3 | semidirect |
| 23. C2×#1143 | C2×C3 | semidirect |
| 25. C2×#1136 | C2×C3 | semidirect |
| 26. #6409 | C2×C3 | semidirect |
| 27. #6383 | C2×C3 | semidirect |
| 28. #6381 | C2×C3 | semidirect |
| 45. ΓL(1,𝔽8)⋊C8 | D4 | semidirect |
| 95. C7⋊C8 | C3×D4 | semidirect |
| 116. C22⋊Q8 | AGL(1,𝔽7) | semidirect |
| 150. ΓL(1,𝔽8) | #468 | semidirect |
| 198. C7 | C3×#468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| ΓL(1,𝔽8)×C22⋊Q8 | 2 |
| C2×#1143⋊C3 | 2 |
| #6493⋊C3 | 2 |
| C2×#1136⋊C3 | 2 |
| #6409⋊C3 | 2 |
| #6383⋊C3 | 2 |
| #6381⋊C3 | 2 |
| #89821 | 3 |
| C3×#468 | 7 |