Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
208 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 3. ΓL(1,𝔽8)×#106 | C2 | semidirect |
| 4. ΓL(1,𝔽8)×#103 | C2 | semidirect |
| 6. C7×#483 | C3 | semidirect |
| 18. C7×#106 | C2×C3 | semidirect |
| 19. C7×#103 | C2×C3 | semidirect |
| 55. #483 | ΓL(1,𝔽8) | direct (N × H) |
| 81. #106 | C2×ΓL(1,𝔽8) | semidirect |
| 82. #103 | C2×ΓL(1,𝔽8) | semidirect |
| 103. ΓL(1,𝔽8) | #483 | direct (N × H) |
| 136. C7 | C3×#483 | 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×C4⋊C4×ΓL(1,𝔽8) | 2 |
| ΓL(1,𝔽8)×#106 | 2 |
| ΓL(1,𝔽8)×#103 | 2 |
| ΓL(1,𝔽8)×C22⋊C8 | 2 |
| C7×#483 | 3 |
| C3×#483 | 7 |