Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
228 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 4. ΓL(1,𝔽8)×C4⋊C8 | C2 | semidirect |
| 5. (ΓL(1,𝔽8)⋊C4)⋊C8 | C2 | semidirect |
| 6. (ΓL(1,𝔽8)⋊C4)⋊C8 | C2 | semidirect |
| 7. C4⋊(ΓL(1,𝔽8)⋊C8) | C2 | semidirect |
| 8. #89611 | C3 | semidirect |
| 25. C7×C4⋊C8 | C2×C3 | semidirect |
| 26. Dic7⋊C8 | C2×C3 | semidirect |
| 27. Dic7⋊C8 | C2×C3 | semidirect |
| 28. C4⋊(C7⋊C8) | C2×C3 | semidirect |
| 111. C4⋊C8 | AGL(1,𝔽7) | semidirect |
| 136. ΓL(1,𝔽8) | #424 | semidirect |
| 178. C7 | C3×#424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1131⋊C3 | 2 |
| C2×C8×AGL(1,𝔽7) | 2 |
| #6435⋊C3 | 2 |
| ΓL(1,𝔽8)×C4⋊C8 | 2 |
| (ΓL(1,𝔽8)⋊C4)⋊C8 | 2 |
| C4⋊(ΓL(1,𝔽8)⋊C8) | 2 |
| #89611 | 3 |
| C3×#424 | 7 |