Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
136 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 39 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. C7×#352 | C3 | semidirect |
| 6. C22×C4×ΓL(1,𝔽8) | C4 | semidirect |
| 11. C22⋊C4×ΓL(1,𝔽8) | C4 | semidirect |
| 26. C22×C4×C7 | C3×C4 | semidirect |
| 31. C7×C22⋊C4 | C3×C4 | semidirect |
| 44. #352 | ΓL(1,𝔽8) | direct (N × H) |
| 86. ΓL(1,𝔽8) | #352 | direct (N × H) |
| 88. C22×C4 | C4×ΓL(1,𝔽8) | semidirect |
| 93. C22⋊C4 | C4×ΓL(1,𝔽8) | semidirect |
| 116. C7 | C3×#352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| ΓL(1,𝔽8)×#123 | 2 |
| ΓL(1,𝔽8)×#100 | 2 |
| ΓL(1,𝔽8)×#99 | 2 |
| C7×#352 | 3 |
| C3×#352 | 7 |